I have had this question in my mind since I first saw it because 1. I fly fish and 2. I had no idea of the answer because everyone calls spent Mayflies spent, there is no other name. but now I think I might have it.
The Mayfly has three stages
When it first emerges from the water (sub imago), full adult (imago) and spent.
The common names are Dun, Spinner, Spent. So for your crossword - Term used for a Mayfly - Dun - if Spent ie finished then DONE
It's ok I have answered my own question.
There is a trout fly called a Spent Gnat that represents a Spent Mayfly.
I learn something new every day. Though why they call it a gnat when a gnat is a completely different fly in colour and size...................