My cousin and aunt owned property together with a rights of survivorship deed. My cousin died, my aunt has dementia and is in a home under Medicaid. I am my aunt's guardian and the court wants me to sell the property. The problem is my cousin had a home equity loan on the property in her name only and the property isn't worth what is owed on the home equity loan. If I sell the property can the new owners get a clear title if the loan isn't paid off?

No. They can't get a clear title if the home is sold. The equity loan must be satisfied in full in order to get a clear title. You may approach the bank about a short sale on the property and see if they will take that option.

No, in fact you can't sell the home for less than is owed, unless the bank agrees ( what they call a short sale)
This loan needs to be dealt with in probate of the cousin who died.

Who ever is the legal guardian of aunt who is in a home.
And some people may end up just walking away from the home, letting the bank foreclose on the home

My cousin and aunt owned property together with a rights of survivorship deed. My cousin died, ... I am my aunt's guardian and the court wants me to sell the property. The problem is my cousin had a home equity loan on the property in her name only ...

Did your aunt agree to anything when your cousin got the loan? Because it is at least arguable that if the bank was only secured by your cousin's interest in the property, and since the cousin's interest in the property ended at her death, your aunt owns the property free and clear; the equity loan is unsecured.

The bank should have insisted that it be a beneficiary of a life insurance policy on your cousin.

Thank you all for your answers. My Aunt has dementia and has been in a home since 2006.