No, there is not such thing as free healthcare in the US. Some states have need-based assistance programs (partially funded federally), but coverage varies widely.

She has a broken leg and the hospital sent her to a women's clinic!? Grrr! I suspect she may need more than your typical basic clinic care, but I can't find any references to free clinics in the usual sources.

If her Mom is living with her and is a legal dependant, she may be able to get assistance through Medi-Cal covering her AND her mother -- which might not solve her current crisis, but if she can get help with Mom's prescription and care costs, she may be able to afford care for herself. Basically, Medi-Cal is a limited version of a public HMO. There are no die-hard income requirements for the lower levels of coverage, but you do have to be able to prove need:

Medi-Cal FAQ and how to enroll