Word for people who don't make their deadline
Solution 1:
The word I use at work is just "late". They're all late.
Unfinisher doesn't exist, but non-finisher does.
Your question is a little ambiguous though. Are you looking for a word for people who do finish, but after the deadline (flaky), or for people who never complete the work at all (non-finisher)?
Solution 2:
Tardy
Occurring, arriving, acting, or done after the scheduled, expected, or usual time; late.
There's also under-performing which doesn't imply anything about deadlines, but describes people who don't meet the expectations.
Solution 3:
A person who regularly fails to accomplish what is expected is often called an underachiever. This is not just limited to lateness but other poor showings.
This author suggests a neologistic phrase time optimist for someone who chronically believes that they have more time than they do.
Solution 4:
The words finisher and deadline are not related, because deadline refers to a date and finisher refers to a state. A person is either a finisher or they are not.
Perhaps finisher vs procrastinator would be the best pairing.
John Smith always finishes before the deadline, but Mary Smith finishes after the deadline. They're both finishers; deadline is just a reference to a date. You have to apply logical rules for it to make any sense.
The opposite of finish is start, but there is no opposite for finisher. You could say Mary Smith is a starter but that has a completely different meaning than the opposite of finisher.
One could say the opposite of finisher is quitter. Since someone who never finishes must have quit.
Furthermore, the question in a way is in error, since a finisher could also be someone who always finishes after the deadline, but at least they always finish.