The default situation is as @Mike9241 calculated.
If there was an expressed understanding that the home was being put in the son's name only for purposes of simplifying inheritance, and the mother had the right to live there until she died and the son has no rights before then, there might be an implied life estate. With a life estate, the heir inherits a full stepped up basis.
Most of the time, life estates are in writing. An implied life estate is valid, but can be difficult to prove if the son is audited, especially if the son didn't even know what was happening at the time, and can't produce letter or emails proving the mother's intentions.
If the mother is still alive and competent to make legal decisions, she and her son should talk to an attorney, especially one with a practice in elder law and estate planning. There are ways to make the life estate clear in writing. (I'm not going to suggest them because if they do it on their own based on free internet advice and something goes wrong, they could be in a worse position.). There are also steps they could take to protect the home and the mother's other assets if she is unlucky enough to need expensive long term medical care, so the son can inherit something instead of being forced to spend all the estate on medical care.
