There is mixed case law as to when a single-person LLC can be treated as alter-ego and/or levied against when the single-person member is a judgment debtor. But you need to review local and national laws, and also provide more details before this question can be answered fully.
The practical answer to your question is contingent on whether or not the Claimant has filed for declaratory relief asking the Court to pierce the veil of the corporation, establishing the corporation as merely an alter ego for the individual. If the LLC had only one or two people and failed to substantiate its autonomy from the single member control, then they may be able to pierce the veil and the writ of garnishment could apply to the successor and/or predecessor in interest, or the individual running the LLC. In sum, it is possible, if the creditor takes certain measures.