 This phase Ib trial studies the side effects and best dose of the CDK46 inhibitor ribociclib when given together with doxorubicin in treating patients with soft tissue sarcomas that has spread to other places or that cannot be removed by surgery. Ribociclib may stop the growth of sarcoma tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as doxorubicin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving ribociclib for a week prior to standard treatment with doxorubicin may work better in treating patients with soft tissue sarcoma. 