What does non-suit mean ,if you have a warrent in debt aganist you ?

Answer 1

This is NOT an informed answer.
'Suit' sounds like a reference to a lawsuit. That would make 'non-suit' mean you are not being taken to court. My guess is they are saying you owe them, but they are not ready to sue. I suspect this is more of a collection tactic than an actual legal term.
Again, this is just a guess based on what I think the words normally mean.