Can Medicaid or the NH take my Mom's life insurance proceeds upon her death?

My mother went into a nursing home on medicaid. I was very upfront about what her assets are. They are aware that she has a low face value life insurance policy. I am the beneficiary. The face value of the policy will not be enough to pay for her funeral. 4 -5 months into her stay at the nh, the financial person asked me who her life insurance policy was with. I told them. I know from medicaid planning seminars I've attended that there is a simple yes or no answer to this question. it just slips my mind whether the answer is yes or no.