There are two sorts of things commonly known as owner financing. One is a contract for deed. Essentially, the owner maintains official ownership while you pay him (and taxes, insurance, etc..). If all goes well when he's paid off, he transfers the deed to you.
The other kind the owner acts like the bank in a traditional mortgage. You get the deed but he records a security interest in the property.
The risky and scary thing is if they are claiming owner financing, but in fact while the owner is doing a contract for deed with you, he's paying a mortgage on the property (wrap). This is fraught with peril for you if for some reason he takes your money and doesn't pay the mortgage.
If you don't make the payments, then things vary but they're typically bad all around.