Nineteen safeties heard their names called last year in the NFL draft. A total of 35 received grades on NFL.com.

University of Connecticut safety Andrew Adams wasn’t even one of them. He didn’t earn invites to the combine or Senior Bowl, and was an afterthought during the pre-draft process. Adams was considered a potential late-round pick, at best. He knew being undrafted was a realistic possibility despite four solid years at UConn.

In retrospect, that is just fine with him, because Adams is the latest proof that the draft extends beyond the seven televised rounds. The New York Giants signed him as a priority free agent after the draft, luring him with a phone call from safeties coach David Merritt instead of a scout.

All Adams did was start 13 games his rookie season.

“I probably wouldn’t want to change anything,” Adams told ESPN earlier this month. “Everything happens for a reason and it kind of gives you that edge.”

Adams played with a chip on his shoulder. He says that is something that will never wane, even after he made a name for himself. Adams still considers himself an undrafted free agent despite starting the third-most games of any rookie safety and more than any of the 14 safeties drafted in Rounds 2-7. Only first-round pick Keanu Neal and second-round selection Vonn Bell started more (14) games than Adams among rookie safeties in 2016.

2017 NFL DRAFT Round 1: Thursday, 8 p.m., ESPN/ESPN App

Rds. 2-3: Friday, 7 p.m., ESPN/ESPN App

Rds. 4-7: Saturday, noon, ESPN/ESPN App

Where: Philadelphia NFL draft home page » • 2017 NFL draft order »

• Mel Kiper's final Mock Draft »

• Todd McShay's final Mock Draft »

• McShay's ultimate draft preview »

• McShay's final prospect rankings »

• Kiper's final Big Board: Top 300 »

• Kiper v. McShay: Head-to-head Mock »

• McShay's biggest needs for all 32 »

• McShay's 2017 All-Satellite Team »

His success – along with the contributions of defensive end Romeo Okwara and wide receiver Roger Lewis – once again highlights the importance of the entire draft process. The drama this week will not end on Saturday evening after the last pick (the so-called Mr. Irrelevant) is announced. There are still more players to be added. Some could be crucial to the short and long-term success of the team.

In six of the past seven years the Giants have found undrafted players who have gone on to start for them, the most successful being wide receiver Victor Cruz in 2010. He developed into a Pro Bowl player and was a key piece on a Super Bowl team.

Adams, 24, can only hope to replicate that success. If his rookie season is any indication, he’s in good shape. He finished with 46 tackles and an interception, and was second among rookie safeties with a Pro Football Focus grade of 79.4, just barely behind Neal (80.8).

The feedback Adams received on his rookie season was encouraging.

“All positive,” Adams said. “They all said I exceeded all their expectations and they were grateful [for] what I was able to contribute to the team. But they’re also looking for growth from Year 1 to Year 2, which I expect. So my focus is on becoming a better football player overall.”

He went to Atlanta this offseason where he worked at the Chip Smith Performance System and actually trained for football instead of the Olympic track and field events necessary for the pre-draft process. Adams tried to take the experience he gained as a rookie – it was a lot after stepping into a bigger role when injuries affected safeties Darian Thompson, Nat Berhe and Mykkele Thompson – and use it to elevate his game. He sees and understands things at a much different level than last year.

Adams worked with a bunch of NFL players at Chip Smith’s. Among them was Buffalo Bills starting quarterback Tyrod Taylor, whose brain he tried to pick to further master the intricacies of his position.

“He kind of told me what he looks at when he’s under center or in shotgun or whatever,” Adams explained. “Kind of little nuances of the game that the offense looks at from a defense.”

He’s going to need every bit of it this season. There is expected to be competition in the Giants secondary, with the Thompsons and Berhe healthy. Darian Thompson likely has an advantage as a third-round pick whom the Giants wanted to start last year before a foot injury derailed his season.

Adams again has something to prove. Thompson know what he's up against. He watched last year as Adams more than held his own, and wasn’t the least bit surprised by the success.

“Absolutely not,” Thompson said. “Andrew and I came in and we played together as the two rookies together in minicamp. It was very evident that he could be a ball player. He’s smart. He’s a smart player. In this defense, especially playing the free safety position, you have to be smart. I wasn’t surprised at all and he stepped in and did a great job.”

Aside from the experience he’s gained, not much has changed for Adams. He still may be overlooked and still views himself as the underdog.

“It is sort of similar to last year. Still an undrafted guy so I need to do everything I can to prove myself and to stand out from others, just like last year,” he said. “Nothing really changed other than I had a year under my belt and I look to become better in Year 2. I’m still focused on standing out and separating myself from other players.”

Even from those who were drafted.