Well, "how" you COULD do it is a very different question from how to entice your family to agree to it... Depending on how the trust is written, who's trust it is, etc. it's usually not too difficult to transfer the property to a family member. You can often do this without triggering a reassessment of value too, depending on the use/occupancy of the home.
If your family is trying to obtain a fair market price, you could potentially just buy the property from the trust and avoid many of the selling costs associated with selling it on the open market/MLS (agent commissions, photos, marketing, etc.). I've also had clients buy the property for a pro-rated amount based on trust beneficiary status when this is happening due to the passing of the trustor.
For example: Fair market value of the house is $500k, owned free and clear, and you are one of 5 beneficiaries of the estate. You apply your $100k worth of inheritance toward the price and just buy the house for $400k paying $100k to each of the other 4 beneficiaries (overly simplified math obviously, but you get the idea).
There could be important legal aspects to any particular trust that I'm not accounting for as well obviously, so I would still suggest consulting a real estate/trust attorney at minimum.