Can you buy a car with bill of sale and lien on it?

No. And not a good idea even if it was.

Yes, you can. If you are buying from a dealership (new or pre-owned) and they have taken the vehicle in as a trade-in then don't pay it off and you purchase it....someone is not going to be happy. Or, if you purchase from an individual who still owes a balance to the lienholder and never pays balance owed, again,.... someone is not going to be happy. As a previous employer of a pre-owned dealership, this does happen...BE SURE, you have the vehicle transferred to you with the seller's name and signature legible. Do a title search!! Why would anyone purchase a vehicle or take over notes and not have the vehicle registered in his or her name? DEFINETLY, not a smart thing to do.