You can apply for a lost title in a Michigan. If you don't own the car the current owner would have to do it. You could probably do the legwork for him, pay the fee and have him sign the application.
Or, you could purchase the car and process the application yourself.
I did it a few years ago on a 71 Pontiac GT 37. Not that hard to do.
http://www.michigan.gov/sos/0,4670,7...6308--,00.html