Hi and welcome to Just Answer!
The fact that you owe taxes to the IRS has no effect on your qualifications to be a dependent - as long as all requirements are met - you may be claimed as a dependent on someone's tax return.
If someone claims you as a dependent - that person will not be liable for your tax debt and his/her refund will not be garnished for your tax debt.
However - that will not eliminate your tax debt.
Let me know if you need any help or clarification.