With Phil's thoughts about tax avoidance clearly in mind, let me address your question directly.

Your parents would need to sell the property to get the exclusion. The buyer can be a related party - a relative.

But the buyer would need to enjoy the benefits and bear the burdens of ownership. IOW, the buyer would get the gains in value or suffer any further losses in value. Those could not be passed back to your parents. So because the market is currently somewhat depressed, they're not going to get as much for the property as they would have a year or two ago. They could have sold then, but didn't. Now the loss in value is their problem. That was a risk of hanging on instead of selling.

One possible scenario would be for a friendly buyer to buy now, with some seller financing. It sounds like the existing loan on the property is either not large if there is one at all. The price could be somewhat generous in exchange for favorable financing terms from the seller.

The downside here is in the intertwining of family finances, and the impact on relationships if things don't work out. Particularly if the buyer doesn't make payments on time.

--Peter