A tax lien will not affect your joining a union. You should be aware, however, that the IRS may levy your wages. You should talk with a tax attorney to resolve this.
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A tax lien shouldn't affect your ability to join the union; after all, it won't automatically make the union liable for your unpaid taxes. However, because the union's benefits funds might get garnishment notices from the IRS once you start accruing benefits, you should consider checking with the union itself to see if they look into anyone's credit history, which is most likely where they would find a tax lien.
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