"the beneficiary would sell it but have no money to pay taxes."

Yes, from the sale.

"This action could mean no tax on a future sale as gain would likely be less than the 250K exclusion"

Is this already the primary residence? The person can't immediately sell and benefit from the exclusion. But if there really is the likelihood of nearly immediate sale, there would be very little gain.

Why doesn't the trust just sell the property and distribute the proceeds? Aren't they setting up this person for more failure?