My husband had a joint bank account with his now deceased mother who was on Medicaid. What happens if he does not repay Medicaid?

Suppose the mother did not incur a debt. Does the remaining amount belong to the other person on the account. ?

But since the letter states that the assets "should" be forwarded, does that mean that not forwarding the assets is an option?

One of the problems with joint accounts is that any money in the account belongs completely to each person that owns the account. In this case, if the mother incurred debt, all money can be used to pay that debt, even if half of it is not hers. If your husband had incurred debt, similarly all money could be used to pay his debt. So yes, the state can take the money.

There is a good thing to know here, and I'm glad that it wasn't so expensive for you and your husband. Joint accounts can be a huge headache when it comes to Medicaid. A spouse would get to keep half, but other people would not. Children shouldn't be putting their own money into the elder's account because of this.