Mortgage amount with forclosed property?

[Account Closed]

For example, you have a person who took out a mortgage of $10,000 for a property.  He continues to pay the monthly mortgage but stops at $5000 and the property is foreclosed.  I don't know anything about the process, but if I bought that property, would I only have to pay the $5000 worth of mortgage instead of $10,000?

If this is true, if the "leftover mortgage" was $1500, and I bought the property, I would only have to pay off that $1500 mortgage instead of $10,000?