This is a bit old, but with the renewed/continuing calls for "mental illness" prohibitions on possession, and California's clear line of reasoning that having guns in the home is possession regardless of who owns them, I wonder if things like Dementia/Alzheimers would also fall under the law as they interpret it.
CDC (blech) seems to consider dementia a mental illness, what I can find of CA's law in terms of prohibition on this particular issue "Is currently under a court-ordered conservatorship because he or she is gravely disabled as a result of a mental disorder or impaired by chronic alcoholism"
I wonder if this then serves to make families choose between taking care of loved ones in their home, and the caretakers right to firearms. I understand CA is essentially a lost cause (still fighting, and never know, someday SCOTUS may come through) but as this is almost surely to come up in many other states, I think it is important to clarify. I've not seen any mention of court cases in this regard, but it seems possible, if not likely that it would impact quite a few.