A debt collector can sometimes garnish your wages if they take you to court and sue you and then win a judgement.
However not all states make it legal for a debt collector to garnish a persons wages to pay back the debt so you'd have to check the laws in the state you live in as to whether the debt collector can legally garnish your wages or not.
But in most states it's not legal for a debt collector to garnish wages however some states do allow it.