What happens if your car is towed but you don’t want it back?

My grandmother in California loaned me her car a few years ago, and then told me to just keep it when I was already home in Seattle. The title is in her name, and I’m having an impossible time getting it from her (she’s very elderly now and doesn’t seem to understand what I need despite me explaining it multiple times). The vehicle was never registered here, and it has since died on the street, been impounded, and is waiting to be towed. I spoke with the officer in charge, and she’s giving me a little extra time to get things in order. I don’t actually want the car back, so whether it’s donated or just taken by a towing company doesn’t matter much to me, aside from my concerns over potentially hefty fines. My grandmother assumes the fines will go to her, and since she’s unlikely to ever visit the state or drive here again, she isn’t too concerned.

So my questions are: (1) what happens if your car is towed in Seattle and you don’t want it back, and (2) is there any way these potential fines could impact me, despite the car not being in my name?