Wrap around Mortgage? Or Assuming loan

[Account Closed]

The Bank will not accept partial payment; it is $12k or Foreclosure; 3rd option - pay off loan or private sell

I was introduced to this opportunity by a friend whose sister has this house and I have heard of these pre foreclosure types like this and need help understanding how it works and how I could help her without being too much of an investor 

would this be a wrap around mortgage, an assumption or flat out new loan

Details:

Person is behind $12k, Owes $91K, Mortgage is $795 PITI. Lived there 8 years, This house is in Murfreesboro Tn

Value is $180s and this market rents between $1200-1600

Don't know the condition of the house yet but the owner wants to continue living there and possibly buy back the house through lease to own close to what she is paying now.

Here are my question:

How does it work - If I work with the bank and pay the back payments ($12k) and assume the loan with a better interest rate (1% difference) does the $12k come off the 91K and would I also have to pay a downpayment since I am getting the loan as an investor? 

This is broad but never had to do this and I am confusing myself