1880 house with small, round basement

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Hello, I am considering buying my next door neighbor’s house. It’s overall footprint and layout is almost identical to my house which was built in 1900. I have a full basement, his house has a very small basement with a rounded, almost circular shape. maybe 6x10 at its widest points? The basement sits under the rear portion of the house. I know this is common in 1800s houses. A home I used to live in built in 1870 had the same type of basement. 

What do you call this type of basement? Does anyone have experiences with this type of foundation? There are a couple areas in both the front and back of the house where the floors are definitely dipping or sloping a couple inches, give or take. The house is missing most of the gutters so that is probably causing problems too. There are definitely major issues, some maybe just from settling, but the small basement area seems dry. 

I would probably run in the opposite direction if this house wasn’t right next to mine. It also has an amazing 2 story coach house behind it that is in better shape than the house. The house has needed a roof for probably 10 years, the water damage is bad upstairs but not as bad as I expected judging by the outside. Otherwise it’s a total gut job. He would let it go for next to nothing. I’m intrigued by the opportunity but it would definitely be a huge headache. Any thoughts? Thanks!