Testing the Combination of Anti-Cancer Drugs Talazoparib and Temozolomide in Patients With Advanced Stage Rare Cancers, RARE 2 Trial

Inclusion Criteria: * Patients must have histologically confirmed rare solid tumors that have progressed on standard therapy or for whom there is no longer standard of care therapy. Other rare tumor types may be acceptable at the discretion of the principal investigator (PI) * Patients must not be eligible for a higher priority study, such as a disease specific study of phase 2 or higher or a randomized study. Specifically, patients with pheochromocytoma and paraganglioma at the clinical center will be eligible for this study if they are not eligible for the NCT04394858 due to prior PARP inhibitor, dacarbazine (DTIC) or temozolomide therapy * Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1, with at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) * Patients consenting to biopsies must have a tumor site amenable to biopsy. If avoidable, the lesion for biopsy should not be selected as a target lesion for RECIST measurements * Prior to entering the study, patients must have: * \>= 3 weeks since completion of radiation therapy or major surgery * \>= 5 half-lives or 3 weeks (whichever is shorter) since completion of biologic therapy or chemotherapy * Should be at least 6 weeks out from nitrosoureas and mitomycin C * \>= 2 weeks since any prior administration of a study drug in a P…