FOXBOROUGH, Mass. -- Quick-hit thoughts and notes around the New England Patriots:

1. On the final day of the NFL draft, coach Bill Belichick smiled when discussing the Patriots' selection of Eastern Illinois linebacker/safety Kamu Grugier-Hill in the sixth round (208th overall), then said jokingly, "You know, Eastern Illinois, it's a school that is closely scrutinized now, but we have some extra help on that one; we have a little scouting going on here. Most teams don't have that extra set of eyes."

That was in reference to Patriots third-year quarterback Jimmy Garoppolo, an Eastern Illinois alum.

That two players from Eastern Illinois (enrollment approximately 9,000) have landed on the Patriots' roster in a span of three years has resonated on campus in Charleston, which is located about 180 miles south of Chicago. Grugier-Hill is the 15th player in program history to be drafted.

"It's obviously big for our school with recruiting," head coach Kim Dameron said. "When we go out and recruit, we start with [alums] like Mike Shanahan, Sean Payton, Brad Childress, Tony Romo and Jimmy Garoppolo. Now there's Kamu. There's a lot of history here, guys who have gone on and done well in the league. That means a lot to the school and community."

Second-year Chicago Bears general manager Ryan Pace is also an alum of Eastern Illinois, which plays at the FCS level out of the Ohio Valley Conference. Late NFL assistant Mike Heimerdinger and current Saints special-teams coordinator Greg McMahon are also among the school's football alumni.

2. How hotly in pursuit were the Patriots of Grugier-Hill? The day before the draft, they quietly flew linebackers coach Brian Flores to meet him for a private workout, mostly to confirm that he was a player on their short list to select entering the draft. Turns out the Patriots weren't alone, as the Raiders, Chiefs, Giants, Cardinals, Lions and Colts were teams that either had Grugier-Hill in for a visit or put him through a private workout before the draft. So while he comes from an under-the-radar program, Grugier-Hill was anything but under the radar to NFL teams in the pre-draft process despite not being invited to the combine. He falls into the category of hybrid safety/linebacker, a profile that is growing in importance around the league as teams are playing more substitution defense than ever before.

3. Dameron served as safeties coach at Mississippi from 2008 to 2010, during which time he coached current NFL safeties Kendrick Lewis (Ravens) and Jamarca Sanford (Saints). That's part of the reason he felt confident telling NFL teams Grugier-Hill has the skill set to succeed in the pros, either as a traditional safety or in-the-box sub linebacker. On top of that, Dameron said he has little doubt Grugier-Hill will be "a fantastic special-teams player. ... He would have been on all four of our special teams had I allowed him to be. But I put on a limit on two."

4. There is a common link between Patriots receiver Julian Edelman and Cowboys receiver Dez Bryant this offseason, as both underwent second surgeries for similar foot injuries. Bryant had surgery Jan. 6 for the same reason Edelman recently did -- a bone graft to strengthen the area around the screw that was inserted as part of the first surgery. By doing so, both players hope it provides the foot more stability, which is particularly important for a receiver like Edelman, who has a knack for quickly changing direction by planting his foot in the ground and exploding. As for the timeline, Bryant is not yet fully cleared but is expected to do more at upcoming organized team activities. As noted last week, the Patriots will naturally take a patient approach with Edelman.

5. In a reminder of how Belichick likes to close ranks, reporters weren't permitted to watch any parts of the team's recently concluded rookie minicamp. The league doesn't require teams to open rookie minicamp practice, and as part of my curiosity, I took a quick poll of reporters around the league to get a feel for how the majority of teams approached their 2016 rookie camp media-wise: 24 gave access to at least one full practice, four allowed reporters in for a limited period of stretching/warm-ups (10-20 minutes), two didn't hold a traditional rookie minicamp (Jaguars, Dolphins) and two had no media practice access at all (Patriots, Saints).

6. I enjoyed Kirk Minihane's most recent "Enough About Me" podcast with Patriots Hall of Fame quarterback Drew Bledsoe, particularly with Bledsoe's thoughts/insight on his relationships with Bill Parcells and Belichick:

On Parcells: "I haven't seen him or talked to him since I retired from the Cowboys [in 2006]. Those relationships aren't always warm and fuzzy. It wasn't warm and fuzzy with Bill, but I'm glad I got a chance to play for him, particularly when I was a young player. But the end of the deal down there in Dallas wasn't super friendly."

On Belichick: "Belichick, he's such an interesting guy, because when you work for him it is all business. Everybody knows that. There is no warm and fuzzy. There's no small talk, none of that. But since I've retired, I've been back there a couple of times for wine deals or to come to a game and he's an entirely different guy when it's not a business relationship. He smiles and he's engaging and interesting. I came back for a wine presentation at the wine shop there at the stadium, and he came over for that and hung out and we talked for a while afterwards. It's actually a pretty decent, pretty friendly relationship."

7a. The connection between the Patriots and Bears has been notable the last few years, with the club swinging multiple trades (e.g. Martellus Bennett, Jonathan Bostic, Ryan Groy), and those relations could be further strengthened before the teams' Aug. 18 preseason game in Foxborough. The sides have been discussing joint practices leading into the game, and at this point, I'd be surprised if they don't happen on the practice fields behind Gillette Stadium. Bill Belichick-John Fox. Tom Brady-Jay Cutler. Say hello to old friends, Shea McClellin, and welcome back to town, Brian Hoyer, Akiem Hicks and Robbie Gould. Those are always fun.

7b. Did You Know: Ben McDaniels, the brother of Patriots offensive coordinator Josh McDaniels, was hired as an offensive assistant with the Bears in February.

8. When deciding to take a significant pay cut to stay with the Patriots, receiver Danny Amendola weighed many factors, and the chance to play again with his former St. Louis Rams teammate Chris Long was one of them. "He's a great teammate and one of my best friends," Amendola said last week, adding that it will be "a lot of fun" to share a locker room again with Long. The two ultimately craved the same thing after some lean years with the Rams -- the chance to play meaningful games into January -- which led them to New England at different points of their careers.

9. With last week's news that the Bills are retiring Bruce Smith's No. 78, it sparked memories of his epic one-on-one battles over a 13-year span (1987-99) with Patriots Hall of Fame left tackle Bruce Armstrong, whose No. 78 is retired in New England. The neat backstory was how they became friends over the years, growing especially close after Armstrong tore his ACL at Buffalo in the 1992 season, and then Smith called him the following day to express his concern. The late Alan Greenberg of the Hartford Courant, as he often did, captured the essence of that friendly rivalry as it was winding down.

10a. As part of the rookie class' orientation/introduction to life as a Patriot, Belichick annually carves out time on the schedule to have the new players visit the team's Hall of Fame. That happened Friday. For most of this year's rookies, who were born in 1993-94, their background with the club starts around 2000, which means they've only known the franchise to have resounding success. But as longtime Patriots fans can attest going back to the team's inaugural season in 1960, it wasn't always like this. Not even close.

10b. Fan voting for the Patriots' Hall of Fame concluded Saturday, so now we wait to see whether it's cornerback Raymond Clayborn, running back Kevin Faulk or linebacker Mike Vrabel who is this year's inductee. The story behind the story: By wearing Brady's jersey and saying his name while announcing the team's third-round draft choice on national television, did Faulk put himself over the top? We should find out early this week.