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 …