I doubt that would happen. Once the electoral college votes, it's all over. If Trump refuses to leave the White House, then the Marine Guards will remove him, because the winner of the electoral college is the real president -- no matter how much crying and whining Trump does.
But there is a way Trump could lose the election and still remain in office. State legislatures determine how electoral college voters are picked, and some GOP state legislatures could ignore the voters and pick Trump electors.
I'd like to think that couldn't happen, but Republicans have shown us lately that they don't care about anything but trying to hang on to power. Morality, ethics, honesty, and rule of law mean nothing to them. If they see both houses of the U.S. Congress lost to Democrats, it's within the realm of possibility that they could override state voting results and move to pick electors that would keep a Republican in the White House.
Here's how Barton Gellman puts it in The Atlantic: