My mom owns a new car, but she can't drive it (dementia). Is there a way I can get it repossessed without owing anything on it?

If you have POA you should be able to either sell the car if you can get enough money for it and or talk the finance company about voluntary repossession. You should at least get the facts straight from them...well they might not tell you all of your options but still you will know all your straight forward options. Then while I don't like to promote shirking financial commitments if there are 3 years still left on the note and she is at the point you describe it doesn't sound like she financed the car that long before dementia hit and you are probably right, harming her credit at this point might be a good thing rather than a bad one. But there are probably financial counselors that even specialize in elderly that might wise to consult too, check your local agency on aging to see what might be available free or at minimum expense, you probably want to think about planning for, being prepared for when she needs more services than you can provide alone or maybe at home too and I'm not sure how all of this might come into play if she doesn't qualify for Medicaid or isn't old enough for Medicare/Medicaid.

I have General POA but she still owes on the car (3 years left). I just got a call today from SS asking if she'd like to draw on her retirement while she waits on her disability claim. She's already claiming SS but the lawyers handling the case say that she can also draw on disability. The extra income would generously help her finances.

Do you have POA. If so you should be able to sell it. The dealer is not dealing with the Dementia person but their assigned POA.

There is no guarentee that you will sell it for what is owed but you have to sell it at blue book value if Mom ever needs Medicaid.