Hello and thank you for allowing me to address your legal question.
When you say that you’re going to move to Delaware, do you mean that you’re going to continue to work in New Jersey? If so, then your wages are subject to garnishment in New Jersey for as long as New Jersey law allows a judgment debtor’s wages to be garnished. It makes no difference that you moved your residence to Delaware. The reason is that the New Jersey courts have jurisdiction over the money while in the New Jersey employer’s hands.
On the other hand, if you were to work for a Delaware company, then the answer may be different since New Jersey would have no jurisdiction over your employer and its money. In that case, you would only be subject to garnishment for as long as Delaware allows. But if you again began working in New Jersey, then you would again be subject to wage garnishment according to New Jersey law (with credit given for the period you paid in Delaware).
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DISCLAIMER: Please understand that the complexities of most legal problems cannot be sufficiently addressed in this setting. Accordingly, my post is intended as general information only, and should neither be construed as specific legal advice, nor as an adequate substitute for the retention of legal counsel.