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Thanks for your question. If the only issue is alimony then it depends on what state the company and you are a resident of. Texas for instance doesn't allow for garnishment for alimony. Other states are different.
If your state allows garnishment of wages-that is the state that you are a resident of allows garnishment for alimony then yes if they pursue to record the matter as an out of state judgement and ask for garnishment. The garnishment of tax refunds should be over as well unless somehow this all was lumped together.
You might want to review the order to see if they divided this out in amounts for alimony as separate from the support. Support in general has many more remedies available to collectors than does alimony. I hope this answers the questions and gives you some ideas in this matter..
Most states including Florida allow for garnishment for child support. Here is a web a page with other things the state can do to you for back support. The alimony might be recordedas ajudgement and they might try creditor type remedies such as crdit bureay, abstract the judgement, etc..