I don't have the will power to really go through and look but I wonder how 2nd round picks are still with their respective teams since 2011.
NFL: average career length | Statista
According to this chart, the average career length for an NFL player is 3.3 years. Since 2011, the Patriots have drafted 9 times in the 2nd round. Dawson (2018), Cyrus Jones (2016), Richards (2015), Garoppolo (2014), Collins (2013), Dobson (2013), Wilson (2012), Dowling (2011), and Vereen (2011). From my count, 6/9 are still in the NFL. That could jump to 7/9 if Cyrus Jones signs on with someone else.
Gronkowski is still with the Patriots but he was 2010, so he doesn't count according to the year choice. Chung as you pointed out is still with the team, and he dates back all the way to 2009.