MIL recently passed. How to handle “estate”?

Location: Los Angeles, CA

Mother in Law passed away about a month ago. My wife (only child) isn’t looking to inherit anything or take control of her bank account. MIL had a few debts that exceed her assets. If we do nothing (which is what we would like to do) does the bank just distribute the assets in MIL’s account towards her debts? Can any of MIL’s debts become our responsibility? FYI: we don’t have any joint accounts, we’ve never co-signed anything with her.

Thanks for your advice!