My Question is: How then (or why) is it that if there is no such thing as free will, there is such a thing as accountability?

Accountability only exists in relation to one's own standards and one's social context. It's completely relative and only exists because concepts defined as real by one's social context have real consequences.

I don't believe in free will but I'm a very strong atheist.

On the original subject I think people who want to take care of her should be allowed to, but her husband should not be required to pay for any of it. I'm sure enough private donations are available to sustain her life at least for a few more years.