Does a bank have any recourse if a homeowner refinances their home and cannot make the payments other than foreclose on the property? If the property doesn’t sale for enough to pay the loan off in full, can the bank take other assets of the homeowners?

In some states, a borrower might owe their mortgage lender money after a foreclosure sale of their home. This is called a "deficiency". However, in most residential foreclosures in CA, the lender cannot go after the homeowner for a deficiency. Yet, there are some exceptions. In CA, foreclosures can be either judicial or non-judicial. Judicial foreclosures are administered though the courts system, while non-judicial foreclosures (the most common type of foreclosure) are handled by a trustee. With a non-judicial foreclosure, a lender cannot get a deficiency judgment and since most residential foreclosures are this type, that means that most people going through foreclosure don't have to worry about being liable to a foreclosing lender for a deficiency judgment. If a lender chooses to pursue a judicial foreclosure, then deficiency judgments are permitted, but the amount of the deficiency is limited as per state statute. However, even if the lender uses judicial foreclosure, deficiency judgments are not allowed in certain cases, again as per statute. Bottom line, in all liklihood your mother will bear no legal liability after foreclosure but to be sure of her situation, she should consult directly wirth a local attorney who can best advise her of her rights.

If the payments aren't made on the mortgage, the lender has three options which they can exercise:
1) Simply foreclose, sell the home, and apply the proceeds from the sheriff's sale (less costs of foreclosure and sale) against the balance due; if the home is worth much more than the balance due, they would even have to return the excess to borrower(s). 
2) Don't both foreclosing, but sue *any* of the borrower's (which includes co-signers) for the money due. Foreclosure is an option lenders have to recover their money, but they are not required to foreclose--they can go straight to suing.
3) Foreclose, sell the home, and if there is a deficit, then sue the borrowers for the balance. Note that even if the home is appraising for more than the loan, if RE values fall, or even if just, for whatever reason, no one wants to pay close to the nominal value at the foreclosure sale, the home could end up going for less than the loan.
There is no way to 100% assure your parent that she is safe; whenever anyone signs a loan, they expose themself to liability.