Niraparib and Dostarlimab for the Treatment of Small Cell Lung Cancer and Other High-Grade Neuroendocrine Carcinomas

Inclusion Criteria: * Participant must have unresected or locally advanced small cell lung cancer (Cohort 1) or high-grade neuroendocrine carcinoma (Cohort 2) confirmed by staff pathologist. High-grade neuroendocrine carcinoma of prostate (e.g. aggressive variant prostate cancer, small cell of prostate, etc.) are excluded * Patients must have had at least one prior line of systemic therapy directed at their malignancy * Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 * Participant must be \>= 18 years of age * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Hemoglobin \>= 9 g/dL * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or calculated creatinine clearance \>= 60 mL/min using the Cockcroft-Gault equation * Total bilirubin =\< 1.5 x ULN (=\< 2.0 in patients with known Gilberts syndrome) OR direct bilirubin =\< 1 x ULN * Aspartate aminotransferase and alanine aminotransferase =\< 2.5 x ULN unless liver metastases are present, in which case they must be =\< 5 x ULN * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or partial thromboplastin (PTT) is within therapeutic range of intended use of anticoagulants. Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Participant receiving corticosteroids may continue as long as their dose equivalent to 10 mg prednisone or less and is stable for least 4 weeks prior to initiating protocol therapy * Participant must agree to not donate blood during the study or for 90 days after the last dose of study treatment * Female participant has a negative serum pregnancy test within 7 days prior to taking study treatment if of childbearing potential and agrees use an adequate method of contraception from screening through 180 days after the last dose of study treatment, or is of nonchildbearing potential. Nonchildbearing potential is defined as follows (by other than medical reasons): * \>= 45 years of age and has not had menses for \> 1 year * Patients who have been amenorrhoeic for \< 2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use an adequate barrier method throughout the study, starting with the screening visit through 180 days after the last dose of study treatment. Information must be captured appropriately within the site's source documents. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient * Pelvic irradiation * Participant must agree to not breastfeed during the study or for 180 days after the last dose of study treatment * Male participant agrees to use an adequate method of contraception starting with the first dose of study treatment through 180 days after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient * Participant must be able to understand the study procedures and agree to participate in the study by providing written informed consent * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial Exclusion Criteria: * Participant must not be simultaneously enrolled in any interventional clinical trial * Participant must not have previously received a simultaneous combination of PARP inhibitor and immune checkpoint blockade (immunotherapy) * Participant must not have had major surgery =\< 3 weeks prior to initiating protocol therapy and participant must have recovered from any surgical effects * Participant must not have received investigational therapy =\< 4 weeks prior initiating protocol therapy * Participant has had radiation therapy encompassing \> 20% of the bone marrow within 2 weeks; or any radiation therapy within 1 week prior to day 1 of protocol therapy * Participant must not have a known hypersensitivity to niraparib and dostarlimab components or excipients * Participant must not have received a transfusion (platelets or red blood cells) =\< 4 weeks prior to initiating protocol therapy * Participant must not have received colony-stimulating factors (e.g., granulocyte colony-stimulating factor, granulocyte macrophage colony-stimulating factor, or recombinant erythropoietin) within 4 weeks prior initiating protocol therapy * Participant has had any known grade 3 or 4 anemia, neutropenia or thrombocytopenia due to prior chemotherapy that persisted \> 4 weeks and was related to the most recent treatment * Participant must not have any known history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML) * Participant must not have a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent * Participant must not have had diagnosis, detection, or treatment of another type of cancer =\< 2 years prior to initiating protocol therapy (except basal or squamous cell carcinoma of the skin and cervical cancer that has been definitively treated) * Participant must not have known, symptomatic brain or leptomeningeal metastases. Patients should have magnetic resonance imaging (MRI) brain with and without contrast (or computed tomography \[CT\] head with and without contrast) within 4 weeks prior to initiation of therapy. If history of known brain metastases, these must be treated with completion of treatment at least two weeks prior to initiation of therapy. Known brain metastases must be clinically stable and asymptomatic * Patient experienced \>= grade 3 immune-related adverse event (AE) with prior immunotherapy * Participant has a diagnosis of immunodeficiency or has received systemic steroid therapy in excess of 10 mg prednisone (or equivalent) or any other form of immunosuppressive therapy within 7 days prior to initiating protocol therapy * Participant has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[qualitative\] is detected) * Participant has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Participant must not have a history of interstitial lung disease * Participant has received a live vaccine within 14 days of initiating protocol therapy