Can your 90 year old father cash in his annuity and make gifts of the funds to his grandchildren if he is currently being considered for Title 19 and is living in a nursing home?

I'm going through this now with my Mom. If he cashes in the annuity, and gives it to anyone as a gift, his eligibility for medicaid will be denied until that amount has been " spent down." In English, let's say the annuity is worth $36, 000, and the average cost for a nursing home is $9,000 a month. If he gives the 36K away, medicaid will make him pay the nursing home himself for 4 months before he is eligible for coverage. The more he gives away, the longer he has to self pay. He would have had to give the money away, or have it out of his name 5 years ago.