Will My Mom Owe the Medical Debt My Deceased Dad Left Behind?

My dad recent passed. But before account he did, he was in a nursing home for about 4-5 months. His medicaid application was pending when he passed. Now it looks like they maybe in the side of denying it. He lived in NYC with my mom and left behi
nd a $30k annuity life insurance and a nominal joint savings account. My mom has a few accounts (CD, savings, annuity, etc...) under her own name without his on there.

If they deny his medicaid application, can the nursing home go after my mom for his medical debt? Can they touch her accounts that don't have his name?