If you owe a landlord money for rent and that landlord takes you to court they can go after your wages and by a court order have your wages garnished.
A friend of mine had it happen to her a few years ago.
She didn't pay back rent and left the rental property and 3 months later she was summoned to court and she lost the court case and the judge ordered her wages to be garnished until the landlord was paid back all money owed.
So yes if the landlord wants to they can take you to court and garnish your wages.