Never are YOU responsible personally for leins on a property if you win it at auction. The liens that might encumber the property are on the property, not you. Now if you own the property after the auction the lien holders can technically depeding on the state and type of lien foreclose on the property to get payment for the judgment amount they are owed.

If it's a foreclosure not a tax lien and the lien that foreclosed and you won the property from is a junior lien, like a HOA/condo association lien, then those other liens can still encumber the property and jeopordize your ownership. In this scenerio you would need to negotiate with the remaining debt holders and work out a deal, or rent the place and defend any litigation until you earn money back.