Will a debt collector sue you on a bought debt?

Yes, he can. Usually they dont. They wait till the end of the state statute of limitation. They sue you usually few months before that time. They will try all tactics to get the money from you, when they see they have no hopes, they take aggressive actions.

You should also check if your pay checks can be garnished or not.
If not, then there is no point to sue you.

Self employed, disabled, unemployed usually cannot be Garnished.

You should also read this

Please search in google for State Statute of limitation.