The IRS has specific rules
for the claiming of a child or a qualifying relative as a dependent. From a reading of these requirements, you can determine if you can claim your dependent as a qualifying child or as a qualifying relative. Whether or not they have a tax lien against them does not matter in deciding whether you can claim them as a dependent.
The IRS will not accept someone claiming a child as a dependent unless these rules are met. The person who is NOT entitled to claim the dependent will have their tax return changed, and possibly audited. The IRS computers match almost perfectly for checking doubly claimed dependents.
The IRS offers a publication that specifically states the requirements for claiming a child as a dependent:
(See "Qualifying Child" section)
Here is an article summarizing the IRS publication:
The key points are - under the qualifying child rules, the child must live with you for more than half the year. Under the qualifying relative rules, the taxpayer must provide more than half of the dependent's total support.
If your claim of the relative as a dependent is legitimate and in accordance with the rules, the tax lien won't matter. And if your claim is NOT within the rules, your claim will eventually be denied, with possible interest and penalties, and again the tax lien won't matter.
Hope these thoughts help.