When a house is sold, are the new owners liable for the mortgage currently on the property?

The sale will not close until the current mortgage has been satisfied. The person facilitating the closing, be it an attorney or a title agency will take the money provided by the buyer (or buyer's bank) and disperse it accordingly. Once the deal is closed, the only mortgage on the home should be that the buyer had taken out to make the purchase.

Added~

The seller cannot sell the home for less than what they owe without either

A. Paying the remainder of the balance out of pocket at closing. Or

B. Having the bank approve a short sale.

If there is a recorded mortgage or other secured loan on the home, that is senior to anything that happens after that. So a buyer would be foolish to pay anything for that, because they would be getting a worthless piece of paper, until such loans are satisfied (paid off) or if done with cooperation of the lender(s). Otherwise the seller could take the money and run, leaving you with nothing.

So when you buy property, you should always get title insurance, or at least have a title search (title abstract) done to make sure that there are no outstanding liens.

The current owner cannot sell a home unless the THEIR mortgage is satisfied by closing. The buyer cannot buy a house that currently has a mortgage ALREADY on it, until the mortgage currently on the property is satisfied. Therefore, your scenario is literally impossible. Quit giving thumbs down to answers that make perfect sense to everyone else but you.

Current owner...well if you sold it then you aren't the current owner. When you sell the house your mortgage gets paid off by the new loan and then the new owners have a responsibility on that loan which is in their name. If you sold the property you shouldn't have a mortgage anymore BUT if you are in the process then you might be liable for that last payment depending on when you sign papers and close the loan.

Thats not possible, there cannot be two people with two different mortgages on the same property. When a property is sold, the money changes hands through lending institutions first. If you buy a property for $100,000 and there is $40,000 of mortgage left on it from the previous owner, Your lender pays their lender $100k, they previous lender takes out their $40k and cuts a check to the previous owner for $60k.

This is done often on enter net auctions such as EBAY. All you purchase is the sellers interest in the property. You do not purchase the banks interest or any liens on the property.

The banks and liens are still against the property and they can take the property unless you pay them off.