Closing on a House with a Mortgage Escrow Process?

[Curtis C.]

Lets say you and a seller agree on a price to a house. They owe 45k on the mortgage and you offer them 55k for the house. You write up the contract and take it into escrow.

What happens next? I assume the title company contacts the mortgage company for a precise pay off amount.

But how are you able to close on the house with an existing mortgage? Does the title company pay off the mortgage at the last step of escrow, closing and funding? Then the mortgage gets paid off, the lien released, and you can take title to the property?

Thanks everyone