You can buy a car for parts with a bill of sale. Same as you would buy a fender or some blinker fluid. Don't need a title for that. You're just buying the entire thing at once, instead of once piece at a time.
I know in some states, you can buy a car on a bill of sale, make it meet all state guidlines to to road worthy, and apply for a title that way. Tow yards do similar stuff, because in MN, after 30-60 days they can legally declare a car abandoned, and take possession. After that it's all about proving ownership of said vehicle (which a bill of sale, or an abandonment clause would do) and apply for a new title. It's a PITA, but it works. Hot rod guys do it with barn finds all the time.