On death, all the assets would be added together, the value of BTL property, his share of the joint property and any cash and possessions.
At that point debts have to be repaid, secured debts take priority, and come ahead of funeral costs.
Guessing there would be a shortfall of about £25/£26K after expenses.
Would the son be able to get a Mortgage to repay the Estate?
Another alternative would be for the father to take a Life Insurance Policy to cover the shortfall, you don't say if this is someone planning way ahead, or thinks the position could arise in the near future.
Transfer of the joint property is a solution, but would be considered void if care home fees were needed. Tax would have to be paid if death occurred within 7 years, but this would be tapered, and there could be CGT depending on/when the son wishing to sell.