can you pay back rent, get on title and then refinance?

[Mason V.]

This may be a little confusing but I'll try to make it clear.

Say a home owner is $4000 behind on their mortgage payments and are just days away from auction. 

Could I pay off the $4000 to stop foreclosure, have them put my name on the title, give them $5000+ to move out, continue making payments on the current mortgage and then refinance under my name asap?

 I am just brain storming an idea right now. Not sure exactly how this would work.