Ribociclib and Doxorubicin in Treating Patients With Metastatic or Advanced Soft Tissue Sarcomas That Cannot Be Removed by Surgery

Inclusion Criteria: * Pathologically confirmed diagnosis of intermediate or high-grade soft tissue sarcoma for which single-agent doxorubicin is appropriate therapy, including but not limited to: * Synovial sarcoma * Fibrosarcoma * Undifferentiated sarcoma * Liposarcoma * Leiomyosarcoma * Angiosarcoma * Malignant peripheral nerve sheath tumor * Pleomorphic rhabdomyosarcoma * Myxofibrosarcoma * Epithelioid sarcoma * Undifferentiated pleomorphic sarcoma * Locally advanced unresectable or metastatic disease with no standard curative therapy available * Archival tumor tissue retinoblastoma-associated protein (pRb) positive by immunohistochemistry (IHC) * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria * All races and ethnic groups will be included; for subjects between the ages of 12-18 years only, body surface area (BSA) must be \>= 1.28 m\^2 * Ejection fraction of \>= 50% by echocardiogram or multi-gated acquisition (MUGA) scan * Female subjects of childbearing potential must have a negative urine beta-human chorionic gonadotropin (beta-hCG) pregnancy test at time of screening and within 14 days prior to planned first dose of ribociclib * Willing to use adequate contraception throughout the study and for 3 weeks after study drug discontinuation * Meets the following standard 12-lead electrocardiography (ECG) parameters at screening (defined as the mean of the triplicate ECGs; ECGs done in triplicate do not have a defined interval between assessments): * Corrected QT using Fridericia's correction formula (QTcF) interval at screening \< 450 msec for males and \< 470 msec for females (using Fridericia's correction) * Resting heart rate =\< 100 beats per minute (bpm) * Absolute neutrophil count (ANC) \>= 1.5 K/cu mm * Platelets (no transfusion within prior 7 days) \>= 100 K/cu mm * Hemoglobin (no transfusion within prior 7 days) \>= 9.0 g/dL * Total bilirubin \< institutional upper limit of normal (ULN), except for subjects with documented Gilbert's syndrome, for which =\< 3.0 x ULN or direct bilirubin =\< 1.5 x ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT) in the absence of liver metastases: =\< 2.5 x ULN; if the subject has liver metastases: \< 5 x ULN * Serum creatinine \< 1.7 mg/dL * Potassium within institutional normal limit (WNL) * Corrected calcium WNL * Magnesium WNL * International normalized ratio (INR) =\< 1.5 * Use of rivaroxaban, apixaban, edoxaban or warfarin is an exclusion criteria; therapy with heparin, low molecular weight heparin (LMWH), dabigatran or fondaparinux is allowed * All prior treatment-related toxicities resolved to =\< grade 1 or are determined to be clinically stable by the investigator * Has completed prior therapies according to the criteria below: * Cytotoxic chemotherapy - at least 21 days since last dose prior to first dose of ribociclib * Small molecule inhibitors - at least 14 days since last dose prior to first dose of ribociclib * Monoclonal antibodies - at least 3 half-lives since last dose prior to first dose of ribociclib; exception: denosumab for bony metastases is allowable * Immunotherapy (e.g. tumor vaccines) - at least 42 days since last dose prior to first dose of ribociclib * Radiation - at least 14 days since last dose prior to first dose of ribociclib * Able to swallow capsules * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy \> 3 months * Ability to understand and the willingness to sign a written informed consent document; subject has signed the informed consent (ICF) prior to any screening procedures being performed and is able to comply with protocol requirements Exclusion Criteria: * Subjects with low grade tumors (histologic grade 1/3) * Histologic diagnosis for which single-agent doxorubicin is NOT appropriate therapy, including but not limited to: * Alveolar or embryonal rhabdomyosarcoma * Ewings sarcoma or primitive neuroectodermal tumor (PNET) * Osteosarcoma * Gastrointestinal stromal tumor (GIST) * Prior systemic therapy with an anthracycline for any indication * Known hypersensitivity to any of the excipients of ribociclib or doxorubicin (including to peanut and soy) * Currently receiving any of the following that cannot be discontinued at least 7 days prior to starting study drug: * Known strong inducers or inhibitors of CYP3A4/5, including grapefruit, grapefruit hybrids, pummelos, star-fruit, and Seville oranges * Medications with a narrow therapeutic window that are predominantly metabolized through CYP3A4/5 * Herbal supplements, such as St. John's wort; the use of marijuana or its derivatives is allowed in States with statutes permitting the use of recreational or medical marijuana * Uncontrolled intercurrent medical condition including, but not limited to: * Uncontrolled infection * Symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III-IV) * Acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) or symptomatic pericarditis within 6 months prior to screening * Uncontrolled cardiac arrhythmia or arrhythmia requiring medication other than beta blocker * Psychiatric illness/social situations that would limit compliance with study requirements * Any other concurrent severe and/or uncontrolled medical condition that would, in the investigator's judgment, cause unacceptable safety risks or compromise compliance with the protocol (e.g. chronic pancreatitis, chronic active hepatitis, etc.) * Concurrent malignancy or malignancy within 3 years prior to starting study drug, except: * Malignancies that have completed therapy and are considered by their physician to be at less than 30% risk of relapse, or * Malignancies not requiring treatment (e.g., RAI stage 0 chronic lymphocytic leukemia \[CLL\]) * Central nervous system (CNS) involvement unless they meet ALL of the following criteria: * At least 4 weeks from prior therapy completion (including radiation and/or surgery) to starting the study treatment * Clinically stable CNS tumor at the time of screening and not receiving steroids and/or enzyme-inducing anti-epileptic medications for brain metastases * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea/vomiting/diarrhea, malabsorption syndrome, or major small bowel resection) * Known history of human immunodeficiency virus (HIV) infection (testing not mandatory); NOTE: HIV-positive subjects on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ribociclib; in addition, these subjects are at increased risk of lethal infections when treated with marrow suppressive therapy; appropriate studies will be undertaken in subjects receiving combination antiretroviral therapy when indicated * Systolic blood pressure (SBP) \> 160 mmHg or \< 90 mmHg at screening; if initial screening SBP is outside of the eligible range, blood pressure may be re-checked after intervention; SBP must be documented as stable and within the eligible range prior to starting study drug * Currently receiving rivaroxaban, apixaban, endoxaban, warfarin or other warfarin derived anticoagulant; therapy with heparin, low molecular weight heparin (LMWH), dabigatran or fondaparinux is allowed; if transitioning from a prohibited anticoagulant, a minimum washout of 7 days from last dose of the prohibited medication is required prior to ribociclib start * Participation in a prior investigational interventional study within 30 days prior to enrollment or within 5 half-lives of the investigational product, whichever is longer * Major surgery within 14 days prior to starting study drug or has not recovered from surgical complications (tumor biopsy is not considered as major surgery) * History of congenital long QT syndrome or torsades de pointes * History of non-compliance to medical regimen or inability to grant consent * Pregnant or nursing (lactating) women; breastfeeding should be discontinued