Here's a short list to demonstrate. Safety Jaiquawn Jarrett, a former second-rounder from the Eagles is now a backup defensive back for the Jets. Tackle Jason Smith was the 2009 second overall pick and was what the Jets got in return for sending Wayne Hunter to Saint Louis, backing up the Jets offensive line in 2012. Aaron Maybin was cast aside by the Bills and played a situational pass rusher role for the Jets in 2011.
Now they have two former Patriots on the roster that were high draft picks. OLB Jermaine Cunningham and CB Ras-I Dowling are both are having good springs in OTAs. New York Daily News' Manish Mehta wrote about Cunningham and Dowling and if and how they might help the team this year.
Here's a section from Metha's piece about Cunningham.
Ryan has challenged the 6-3, 255-pound Cunningham at the backup SAM (strong side) linebacker spot, testing him mentally to do a variety of tasks like stopping the run, dropping into coverage and shadowing tight ends. “I’ll be shocked if he’s not a contributor for us,” Ryan said.Maybe as the Jets build back their talent level on the roster they will have to do less and less of this, but there's no harm in bringing in players who might have been drafted highly elsewhere and giving them a modest contract to see if they can carve out a spot on the team, even if just for a year or two. Even more so when that player is a defender considering Ryan's ability to coach a defense and use players to their strengths. If he can pass the eye test with Ryan, it's probably worth a shot.
“I don’t know what happened to him in New England,” veteran outside linebacker Calvin Pace said. “But I do know a lot of people come and go up there. It could be anything… but the talent is there. He’s welcomed here. I know he can help us.”
Ras-I Dowling has had a good spring and has the athleticism, size and instincts to be a successful press cornerback. But Dowling's durability has long been in question. As for Cunningham, he's had some injury concerns too, spraining his MCL and having some hamstring issues during his time with the Patriots.
Calvin Pace will see the most snaps at the SAM spot, Antwan Barnes is coming back from an ACL tear and the team drafted two potential future contributors in Trevor Reilly and IK Enemkpail, but a player like Cunningham has the athleticism, NFL experience and will be playing with one of the league's best front sevens which could make life easier for him.
For both Cunningham and Dowling, we will have to see how they play in the preseason but both players are viable options to make the final roster if they can keep the progress up and stay healthy.