If a husband goes into a nursing home, can they go after the wife's savings even tho he is not on the account. She is also not on the deed.

yes - unfortunately, but is not as if someone or some agency "goes after" any of the money.  what happens is that a certain amount of the couple's assets are required to be used for the person's care.  there are certain assets that are not included, and the spouse who is still in the community gets to keep a certain amount, but the assets must be used for care, and when those assets run out then the person becomes eligible for Medicaid.