I came across an article that claimed there was precedent for a senate trial for someone who left office. It was just a paragraph and the writer left it at that.
I looked it up and have confirmed that such a thing did happen.
https://en.wikipedia.org/wiki/William_W._Belknap
In 1876, William Belknap, Secretary of War in the Grant administration, resigned on the day the House impeached him for alleged corruption. the senate held trial and acquitted him.