You may be able to claim your girlfriend as a Qualifying Relative dependent if:

• You provided more than half of her support in 2016
• She earned less than $4,050 in gross taxable income. (Social Security income generally doesn’t count here.)
• She lives with you 365 days in the year or is related to you.
• She isn’t a dependent on someone else’s tax return.
• She isn’t filing a tax return with a spouse (married filing jointly).
• She  is a U.S. citizen, resident alien, national, or a Canadian or Mexican resident

You can’t claim a dependent if you are a dependent on someone else’s taxes

See Rules For Claiming Dependents

The IRS will not hold you responsible for her debt.