Will my husband become incarcerated if he hasn't paid restitution in 7 years? How?

By failing to pay restitution, he may have violated his probation and there may be a bench warrant issued for his arrest. I suggest that you contact an experienced criminal defense attorney for a face-to-face consultation and give him/her all of the facts surrounding your husband's situation. (S)he would then be in a better position to analyze his case, (and) advise you of his options.

You should hire a lawyer for him to go to court to recall the warrant. A lawyer can do this without him present if the underlying charge is a misdemeanor, so it is less risky for him.