It is not likely that you will be legally responsible for your mother's final medical bill -- although the doctors and hospitals may attempt to collect from you.
In general, you would be personal liable for your mother's debts only if:
- you agreed in advance to be personally responsible, such as by co-signing or guaranteeing a particular transaction
- you are liable for the debts because of another legal relationship that results in a duty of support, such as you claim your mother as a dependent, or
- your negligence caused the debt, which does not sound likely in this case.
The fact that there was no probate should not have any effect.
But because we’re talking about the law, we also have to talk about loopholes. There are some instances in which adult children may be held liable for a parent's debts at death if the parent is considered legally indigent and the child is not considered to be indigent.
Lately, there has been much confusion over these provisions, however, and many reported instances of doctor's and medical institutions harassing people for payment just because they can. Because of this, if you are being asked to pay the bills, it may be worth your while to have a lawyer eyeball the specifics of your situation and how the bills were charged and incurred.
If you're not in touch with an elder law lawyer you might want to begin a search at California’s LawHelp. This website also provides referrals to agencies that may provide free or low-cost legal help.