I think you're mixing up capital acquisitions tax CAT and capital gains tax (CGT). CAT applies to gifts and inheritances, CGT applies to selling things for more than you paid for them.
If the house is sold while the owner is still alive, there will likely be some CGT to pay, as the house was rented out while the owner was in a nursing home.
This is a bit oversimplified but should give you the idea. The difference between the selling price and the price originally paid to buy the house is the gain. You get PPR relief (principal private residence) on the percentage of the gain equal to the amount of time the person lived in the house. CGT is charged at 33% on the remaining gain.
So for example, a house is sold for 300k, was bought for 100k, the person owned it for 20 years and lived in it for 15 years:
The gain is 200k (300k-100k)
PPR relief is 75% (15yrs/20yrs)
CGT is charged on 200k*25% = 50k
50k @33% = 16.5k tax.
As I say, this is oversimplified. There may be indexation, selling and acquisition costs, enhancement expenditure, annual exemption, etc. to take into account as well.