If you're of the age or condition where you're living in a retirement home, there's likely the additional costs of at-home care, panic / fall systems, etc. to add to your "living in a house" costs.

Nothing is cheaper than another thing if you arbitrarily remove a sufficient almost of the cost. If you have equity you can use that to pay for your apartment.

But what parent was saying is that a small assisted living apartment is cheaper than a big unassisted house.