I am not licensed to practice law in Ohio so the following should not be taken as legal advice but simply as information intended for educational purposes and to be helpful.
There are lawyers who specialize in something called "Medicaid planning." The answer to your question is not simple and only a lawyer familiar with the specialty of Medicaid planning will be able to help you evaluate the situation based on all the facts and competently advise you on the range of options that may exist. Your state bar association ought to be able to refer you to a Medicaid planning lawyer who can assist you.
I do practice Medicaid planning in Ohio. As previously noted, Medicaid planning is very complicated. Here are some general answers, but without meeting in person, I cannot tell you this will work in YOUR case.
Generally, if a person in in a nursing home and the cash and other assets are reduced to below $1500, the house needs to be liquidated. However, if the house was your father's personal residence prior to entering the nursing home, the house can be exempted for 13 months and Medicaid obtained once the rest of the money is gone. However, if the house is owned in a living trust, the exemption will not work. The house has to be transferred out of the trust back to your father's name alone for the exemption to be allowed.
Then, once Medicaid is allowed because the money is gone and the house is exempted, after 13 months the house has to be sold. Once the sale proceeds are received by your father, he will lose his Medicaid because his assets now exceed $1500. At that point, there are various options. For example, repay the sale proceeds to Medicaid and continue benefits or undertake some even more complicated planning to try to protect some of the proceeds. I would have to actually meet with you to flesh out the options.
It is very important to get good legal advice from a Medicaid planning/Elder law attorney. I would be happy to assist if you wish.