Originally Posted by Centerline
...Best option is NOT TO BUY a vehicle...where the current owner refuses to apply for a lost title. Chances are very good ITS STOLEN!
This part of your post immediately raised my antennae as well. If I were you I would offer to pay whatever state fees are required for securing a lost title and if the current owner still balks, I'd walk away from the deal. Something's fishy. Replacement titles are a straightforward process in most states...providing there is nothing to hide.
I also second Centerline's warning about using another vehicle's title to title your's, This is not legal and if caught, "the consequences will never be the same" so to speak.
As noted, you might also have the possibility of a bonded title. Be aware that these are only accepted in certain states. Your DMV office or the bonding company will tell you immediately if you can use this process in your situation. In fact, most of the bonding companies on the web (at least the good ones) will have a section on their site listing out the states where their bonds are accepted. But as Centerline suggests, make sure BEFOREHAND that you can do this. Also, this process usually costs over $200. So a replacement title is much more economical.