Unfortunately, some people do get divorced to try to protect assets from long-term care costs. In your father's case, there's the immediate question of who's responsible for paying his assisted
living costs. If he's paying privately -- meaning, without Medicaid assistance -- then his wife may be liable for those costs under North Carolina law. Divorcing him might get her out from under that responsibility.
If Medicaid pays for his long-term care costs, either at a qualifying assisted living facility or at a nursing home, the question of assets is a little different. Anything his wife had as a separate asset before they were married would not count toward his Medicaid eligibility for long-term care costs, and would not be subject to Medicaid repayment rules. So, whether she'd "need" a divorce would depend on how many of her assets are separate and how many are jointly held with your father.
Since they are already living apart, filing papers for a "legal separation" -- one step short of divorce – might also be possible to protect her assets. And even if she does file for divorce, there doesn't seem to be any reason to "cut all ties" with your father. She could go through the legal formalities of the divorce but keep the matter private between her and your father, and in every other way keep up her relationship with him.