If you are talking in any way about federal taxes, no, they get taxed on the capital gain from the sale.

The purchase price is incredibly important when talking about tax implications in real estate. As a matter of fact, it's one of the (if not the) most important aspects of a real estate deal.

If they buy the house for 300,000 , their tax basis in the house is 300,000.

If they sell it for 1.5mil, their gain on the house was 1.2mil. That's the amount that gets initially looked at.

If you're single and sell your house, you may gain up to 250,000 that is not taxed at all, then the remainder is taxed at the current capital gains rate.

If you're filing as married/joint, you can whack 500,000 off the gain and then are taxed on the rest.

You do not get taxed on the market value in any way. You are taxed on the gain at the time of sale, minus the single/married amounts.