I know this will rarely happen, but I was thinking about it last night, and I was wondering what people would rule about it.

If It is the second last day, or last day, and someone follows up a testimonial lead and removes that suspect from the game and that suspect has hits on them, and then Floyd draws his light card that moves a suspect to The Church of St. Theresa and removes all the hits on the suspect, can Floyd play the card or has the suspect left town and can no longer be saved by Floyd?

I would rule that the suspect has left town and is beyond Floyd's reach.

I think you are getting tgestimonial leads mixed up with suspects.  Followed-up leads are removed from the game but this does not mean the corresponding suspect is out of the game.  You can still deal with the suspect sheets as normal adding and removing hits as allowed.

Or maybe I misunderstand the question.

That is correct. However, Floyd cannot fulfill the first duty of the card by moving the suspect. Nevertheless, I believe he can still remove the hits. He just doesn't move the suspect.