The best example of this would be Lance Moore.
Moore was undrafted out of Toledo and stayed in the state of Ohio by signing on with the Cleveland Browns. Later that year, the Saints signed Moore off of the Browns practice squad and onto their own. In that immediate offseason, New Orleans sent him to NFL Europe (remember that, guys?) and, by the time he came back, he was ready to be molded into the player you see today.
With that example in mind, I tried to look at the players who could have the same type of meteoric rise that Moore had, and here are the guys that I came up with.