All the answers here are possibles for your own situation. If you phone me at 585.223.4449, I can give you the 1 best answer for your needs. There's no obligation, of course.
If your question was: "Is it possible to buy a house if the original owner--the seller--still is responsible for the mortgage?" the answer is yes. You can buy the house "subject to" the existing mortgage. It's like assuming a loan when the loan isn't assumable. The person deeds the house to you. You agree with the seller to continue paying the mortgage. But the original owner is still responsible to the bank for those mortgage payments. "Subject tos" can be tricky. For example, if you stop paying, the bank goes after the original owner. Even if you keep paying, there's almost certainly something in the owner's mortgage (called a "due on sale clause") that allows the bank to call the loan immediately due and payable. It doesn't happen too often, but it's a risk.
Hope that helps.