Lien on Property - OR

If Person A takes ownership of a property and later discover there was a lien in the previous owner's name, Person A becomes liable for that lien. So the original owner is off the hook?

Let's say the Owners has several properties. One property is transfered into the name of a family member, Person A. While processing the paperwork, A learns that there are several liens against O to the tune of $30,000. A is told that he will become responsible for those liens if he takes ownership of the property.

So doe that mean that the Owner is free to sell his other properties without a care?