If you owe money to someone, any right you have to receive money (with very limited exceptions) can be subjected to execution by the judgment creditor. The judgment creditor can use whatever sources of recovery are available and does not have to pick one at a time. Garnishment is one way. Execution on assets is another. Both at the same time are perfectly acceptable. The judgment creditor can continue doing this until the debt is paid in full.
Good luck to you.
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The government certainly can take the money, but I wouldn't let that detour you from trying to claim it. If they take it, that puts you one step closer to paying your debt. If they do not, you can use your judgment on whether to give it to them anyway to get closer to paying the debt.