The Jets probably didn't think they would get a talent like Taiwan Jones without spending a draft pick on him. I personally had a 5th round grade on Jones and it seems as though I wasn't the only person surprised to see him go undrafted:
Todd Bowles commented:
I was surprised Taiwan Jones from Michigan State wasn't drafted. He showed some good stuff on film. He's a thumper. He's a pretty heady ballplayer coming in and I was kind of happy to have him when I saw him just because I thought he was getting drafted. No knock against the rest of them, but that's what I saw, he's one of the guys I looked at.
60 tackles, 12.5 for a loss, 4 sacks in 2014 and 67 tackles, 7 for a loss in 2013. That's not for a second tier team, the Michigan State defense is renowned for being one of the toughest units in college football and attracting some of the most impressive defensive talent too.
He's a downhill run stuffer who brings the hammer, he's excellent against the run and can take on and shed blockers. I thought he showed a good ability to sift through traffic to the ball carrier while at Michigan State and while he's not the most athletic players in space, he still has more than enough potential to play a bit part role on this defense while excelling on special teams.
I was extremely surprised to see him go undrafted, but I'm very happy we were able to nab him as a priority UDFA.