I am buying furniture from a party. What if they never paid the original seller?

Maybe.  The furniture store, or financing company, may have a security interest in the furniture if it has not yet been paid for, and/or the right to repossess the furniture if it was not paid for.  As a general matter, if you buy something, and have no reason to know that there may be a problem with the seller's title, you are considered a bona fide purchaser for value, and have good title against any claims.  The real owner would have to go after the person who sold it to you.  However, if you know, or should know, that there may be a problem with title when you buy the property (for example, the furniture store recorded a lien against the furniture), you buy it subject to that mortgage even if you didn't actually know about it), you take the risk that someone with a claim on the property (here the furniture store) may challenge your transaction or have the furniture sold to satisfy the amount it is owed.  If you lose the furniture, you can sue your seller, but he may not have the money to reimburse you.  I don't know why you think there may be a problem with the previous tenant's ownership of the furniture, but if you know about the problem and decide to buy anyway, you may take the risk of the furniture store being able to get the furniture back from you, or satisfy the previous tenant's obligation by selling the furniture.