Legal Question in Real Estate Law in California

This is a good question and a proper answer requires a somewhat more in-depth answer than is possible from the facts given, but let's look at some of the basics.

First, very often, only the debtor's interest in the co-owned real property is in jeopardy. Your MIL's creditors probably couldn't levy or foreclose on your interest in the property, whatever it may be (perhaps a half interest as joint tenants?). In turn, creditors are somewhat reluctant to foreclose on a half interest, because half interests in real property, especially single-family homes, are illiquid and not useful.

Next, you are right that being a co-owner "on title" is conceptually different from being a co-borrower (co-obligor) on a loan secured by the property. It is somewhat unusual for a loan to be made without the pledge of the entire property as collateral. It's possible the MIL pledged her interest in the collateral (the house) without becoming a borrower, and also possible that the loan is not secured by her interest. A third possibility is that the loan was taken out before the MIL's ownership interest was created.

Further, you are right that a transfer of the MIL's interest to your wife, or to your wife and you, would bear some of the hallmarks of a fraudulent transfer, if done for well under the fair market value of the interest transferred. Bear in mind that both the transferor and the transferee can be held liable to injured creditors - they are held to be "in pari delicto."

If you do transfer the MIL's interest by quitclaim, have the father-in-law also quitclaim any interest he may have acquired under community-property laws.

Although lacking details about the terms or timing of the existing financing, I join you in doubting that the father-in-law's assertion about a need for refinancing is correct, but doing so may be a good economic move.

Almost all home-ownership transactions have tax consequences (property tax, gift tax, estate tax, and/or capital-gains tax issues abound) that should be reviewed beforehand with a competent tax advisor.