Larotrectinib in Treating Patients With Previously Untreated TRK Fusion Solid Tumors and TRK Fusion Relapsed Acute Leukemia

Inclusion Criteria: * Patients must be =\< 30 years of age at the time of study entry * COHORT A: Patients must have a histologic diagnosis of infantile fibrosarcoma with an NTRK1, NTRK2, or NTRK3 fusion identified in a Clinical Laboratory Improvement Act/College of American Pathologists (CLIA/CAP) certified laboratory. Fusions may be identified by fluorescence in situ hybridization (FISH) or molecular techniques (reverse transcriptase-polymerase chain reaction \[RT-PCR\] using primers flanking the fusion junction or next generation sequencing). For fusions identified by FISH, an ETV6 rearrangement is sufficient for eligibility in Cohort A. Identification of the upstream TRK fusion partner is not required. * COHORT B: Patients must have a histologic diagnosis of any solid tumor other than infantile fibrosarcoma, including central nervous system (CNS) tumors but excluding high grade gliomas. An NTRK1, NTRK2, or NTRK3 fusion must be identified in a CLIA/CAP certified laboratory. Fusions may be identified by FISH or molecular techniques (RT-PCR using primers flanking the fusion junction or next generation sequencing). For fusions identified by FISH, there must be an identified rearrangement in NTRK1, NTRK2, or NTRK3 (e.g., an ETV6 rearrangement is not sufficient for eligibility) unless the patient has a diagnosis of congenital mesoblastic nephroma in which case an ETV6 rearrangement is sufficient for eligibility. Identification of the upstream TRK fusion partner is not required. * COHORT C: Patients must have a histologic diagnosis of relapsed or refractory acute leukemia with an NTRK1, NTRK2, or NTRK3 fusion identified in a CLIA/CAP certified laboratory. Fusions may be identified by FISH or molecular techniques (RT-PCR using primers flanking the fusion junction or next generation sequencing). For fusions identified by FISH, there must be an identified rearrangement in NTRK1, NTRK2, or NTRK3 (e.g., an ETV6 rearrangement is not sufficient for eligibility). Identification of the upstream TRK fusion partner is not required. * SOLID TUMORS (COHORTS A AND B): Patients must have measurable disease. Patients must have disease that cannot be completely resected without a predicted functional, neurologic, or significant cosmetic deficit in the opinion of the investigator. * LEUKEMIA (COHORT C): Patients must have \>= 5% blasts in the bone marrow. Extramedullary disease is permitted. * Patients must have a Lansky or Karnofsky performance status score of \>= 50, corresponding to Eastern Cooperative Oncology Group (ECOG) categories 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age. NOTE: Neurologic deficits in patients with CNS tumors must have been stable for at least 7 days prior to study enrollment. Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * COHORTS A AND B: No prior anti-cancer therapy, including radiotherapy, other than surgical resection is permitted. * Patients who experience recurrence after surgery alone and no other anti-cancer therapy will be eligible. * If not eligible due to prior anticancer therapy, patients may be eligible for the larotrectinib arm of Pediatric MATCH (APEC1621A) or treatment with commercial larotrectinib off study. * COHORT C: Patients with relapsed leukemia (Cohort C) must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, e.g. blood count criteria, the patient is considered to have recovered adequately. * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive. * A waiting period prior to enrollment is not required for patients receiving standard cytotoxic maintenance chemotherapy (i.e., corticosteroid, vincristine, thioguanine \[6MP\], and/or methotrexate). * A waiting period is not required for patients receiving a single dose of intrathecal methotrexate, hydrocortisone, and/or cytarabine within 7 days prior to enrollment. * \>= 14 days must have elapsed after the completion of other cytotoxic therapy, with the exception of hydroxyurea, for patients not receiving standard maintenance therapy. Additionally, patients must have fully recovered from all acute toxic effects of prior therapy. * Note: Cytoreduction with hydroxyurea must be discontinued \>= 24 hours prior to the start of protocol therapy. * Anti-cancer agents not known to be myelosuppressive (e.g., not associated with reduced platelet or absolute neutrophil \[ANC\] counts): \>= 7 days after the last dose of agent. * Anti-cancer agents that are antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1. There is an exception for blinatumomab infusions, for which patients must have been off for at least 3 days and all drug related toxicity must have resolved to grade 2 or lower as outlined in the inclusion/exclusion criteria. * Corticosteroids: If used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid. A waiting period prior to enrollment is not required for patients receiving corticosteroid for leukemia therapy/cytoreduction. * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor. For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. The duration of this interval must be discussed with the study chair and the study-assigned research coordinator. * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors ). * Stem cell infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: \>= 84 days after infusion and no evidence of graft versus host disease (GVHD). * Autologous stem cell infusion including boost infusion: \>= 42 days. * Cellular therapy: \>= 42 days after the completion of any type of cellular therapy (e.g., modified T cells, natural killer \[NK\] cells, dendritic cells, etc.) * Radiation therapy (XRT)/external beam irradiation including protons: \>= 14 days after local XRT; \>= 150 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial BM radiation. * Radiopharmaceutical therapy (e.g., radiolabeled antibody): \>= 42 days after systemically administered radiopharmaceutical therapy. * Patients must not have received prior exposure to TRK inhibitors (including larotrectinib, LOXO-195, entrectinib, lorlatinib, crizotinib, or lestaurtinib). * For patients with solid tumors without known bone marrow involvement: Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 (within 7 days prior to enrollment). * For patients with solid tumors without known bone marrow involvement: Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment). * For patients with solid tumors without known bone marrow involvement: Hemoglobin \>= 8.0 g/dL at baseline (within 7 days prior to enrollment) (may receive red blood cell \[RBC\] transfusions). * Patients with solid tumors with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts above (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions). These patients will not be evaluable for hematologic toxicity. * For patients with leukemia: Platelet count \>= 20,000/mm\^3 (within 7 days prior to enrollment) (may receive platelet transfusions; must not be known to be refractory to red cell or platelet transfusion). * For patients with leukemia: Hemoglobin \>= 8.0 g/dL at baseline (within 7 days prior to enrollment) (may receive RBC transfusions; must not be known to be refractory to red cell or platelet transfusion). * For patients with leukemia: These patients must not be known to be refractory to red cell or platelet transfusion. * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows (within 7 days prior to enrollment): * 1 month to \< 6 months (male 0.4 mg/dL, female 0.4 mg/dL) * 6 months to \< 1 year (male 0.5 mg/dL, female 0.5 mg/dL) * 1 to \< 2 years (male 0.6 mg/dL, female 0.6 mg/dL) * 2 to \< 6 years (male 0.8 mg/dL, female 0.8 mg/dL) * 6 to \< 10 years (male 1 mg/dL, female 1 mg/dL) * 10 to \< 13 years (male 1.2 mg/dL, female 1.2 mg/dL) * 13 to \< 16 years (male 1.5 mg/dL, female 1.4 mg/dL) * \>= 16 years (male 1.7 mg/dL, female 1.4 mg/dL) * For patients \< 1 month of age, serum creatinine levels must be \< 1.5 x the treating institution's creatinine upper limit of normal (ULN) for patients \< 1 month of age or the creatinine clearance or radioisotope GFR must be \>= 70 mL/min/1.73 m\^2. * Patients with solid tumors: Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age (within 7 days prior to enrollment). After approval of the study chair or designee, infants with a higher total bilirubin due to physiologic or breast milk jaundice are eligible if the conjugated (direct) bilirubin is =\< 2 mg/dL. * Patients with solid tumors: Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 135 U/L (within 7 days prior to enrollment). For the purpose of this study, the ULN for SGPT is 45 U/L. * Patients with solid tumors: Serum albumin \>= 2 g/dL (within 7 days prior to enrollment). * Patients with leukemias: Conjugated (direct) bilirubin =\< 1.5 x upper limit of normal (ULN) for age (within 7 days prior to enrollment). * Patients with leukemias: SGPT (ALT) =\< 225 U/L (within 7 days prior to enrollment). For the purpose of this study, the ULN for SGPT is 45 U/L. * Patients with leukemias: Serum albumin \>= 2 g/dL (within 7 days prior to enrollment). * Patients with seizure disorder may be enrolled if on a stable antiepileptic regimen for \>= 14 days and well controlled. * Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5) except tendon reflex decreased resulting from prior therapy must be =\< grade 2. * All patients and/or their parents or legal guardians must sign a written informed consent. * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met. Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study due to risks of fetal and teratogenic adverse events as seen in animal/human studies, OR because there is yet no available information regarding human fetal or teratogenic toxicities. Pregnancy tests must be obtained in girls who are post-menarchal. Female patients of reproductive potential may not participate unless they have agreed to use a highly effective contraceptive method for the duration of study therapy and for at least one month after the final dose of larotrectinib. Males of reproductive potential with a non-pregnant female partner of child-bearing potential must use a highly effective contraception for the duration of the study and for at least one month after the final dose of larotrectinib. Because of the unknown risk of larotrectinib in nursing infants, nursing women should discontinue breastfeeding during treatment with larotrectinib and for 3 days following the final dose. * Patients with solid tumors, including CNS tumors, requiring corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible. Patients with leukemia may receive systemic corticosteroids for cytoreduction up to 24 hours prior to the start of protocol therapy. If used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid. * Patients who are currently receiving another investigational drug are not eligible. * Patients who are currently receiving other anti-cancer agents are not eligible \[except leukemia patients receiving corticosteroids or hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy\]. Patients with leukemia should receive a single dose of intrathecal cytarabine, hydrocortisone, and/or methotrexate within 7 days prior to Day 1 of Cycle 1 at the time of the baseline lumbar puncture. * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial. * Patients currently receiving a strong CYP3A4 inducer or inhibitor are not eligible. Strong inducers or inhibitors of CYP3A4 should be avoided from 14 days prior to enrollment to the end of the study. Note: CYP3A4 inducing anti-epileptic drugs and dexamethasone for CNS tumors or metastases, on a stable dose, are allowed. * Patients with malabsorption syndrome or other conditions that significantly limit enteral absorption are not eligible. * Patients who are unable to swallow capsules or liquid and do not have gastric access via a nasogastric or gastrostomy tube are not eligible. * Patients who have an uncontrolled infection are not eligible. * Patients who have received prior solid organ transplantation are not eligible. * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible. * Patients with high grade gliomas (HGG) are not eligible.