Impeachment
An interesting consideration is that an ex-President does not have the White House legal counsel or the Justice Department to help defend himself. Or does he? It would be odd, since there is a new President who is their boss. The new President should really volunteer the resources for the old one, though.
We should perhaps distinguish between the two cases of a President who resigns in the middle of an impeachment and the President whose term ends naturally. A reasonable position might be that the proceedings continue if the President resigns in the middle of them, but expire if his regular term expires. I might write on this.
Ferguson v. Maddox, the Pa Ferguson Texas case from the 1920's, and the Impeachment After Leaving Office article that discusses it. Ferguson resigned after his impeachment but before his Senate trial. He was impeached after he started a big fight with the President of the University of Texas. In 1924 he wanted to run again, but his wife, Ma Ferguson, ran in his place because the Texas Supreme Court ruled that his Senate trial was valid and disqualified him from office. She ran against the KKK's candidate and won.
When Belknap's case was exhibited to the Senate by the Housemanagers, it was framed as articles of impeachment against "WilliamW. Belknap, late Secretary of War."' That first sentence wouldprove the entirety of the issue for a minority, but a determinativenumber, of senators. --Jonathan Turley, "Senate Trials and Factional Disputes: Impeachment As a MadisonianDevice," Duke Law Journal 49, no. 1 (October 1999): 1-146
"Review: Impeachment, Attainder, and a True Constitutional Crisis: Lessons from the Strafford Trial," Craig S. LernerSource: The University of Chicago Law Review, Autumn, 2002, Vol. 69, No. 4 (Autumn, 2002), pp. 2057-2101 https://www.jstor.org/stable/1600627
