The day after June 1 has great importance for many NFL teams because it marks the official release of any players who were cut with a post-June 1 designation throughout the offseason, freeing up salary space. When a player is designated for that kind of cut, the organization can distribute the dead-cap hit over two seasons starting on June 2.
Below are five free agents whom the NFL teams that cleared cap space with the post-June 1 designation may choose to sign.

Five players that could be signed after NFL's post-June 1 cap relief hits
1) Justin Simmons, safety
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Justin Simmons is a 30-year-old safety who played with the Denver Broncos until this offseason. He is perhaps the top unsigned free agent ahead of the 2024 season.
Simmons just finished a season in which he recorded 70 tackles, three interceptions and eight passes defensed while playing for the Broncos. For that performance, he was selected to the Second Team All-Pro for the third time in a row.
Some teams, like the Baltimore Ravens, may have Simmons high on their list of priorities. The organization has released cap space after allowing wide receiver Odell Beckham Jr. to depart earlier in the offseason. Baltimore recently lost Geno Stone in free agency and seems to be searching for additional depth at safety.
2) Stephon Gilmore, cornerback
Stephon Gilmore was named the league's best defensive player during the 2019 campaign. Four years later, at 33, he will still be a valuable addition to many league teams at cornerback.
Although Gilmore is not as good of a shutdown cornerback as he previously was, he is still a reliable starter. Gilmore started opposite Da'Ron Bland for the Dallas Cowboys last season. He only allowed four throw touchdowns while recording 13 passes defended and two interceptions.
3) Steven Nelson, cornerback
Steven Nelson has been dependable and steady at the cornerback position over the past few years. Teams in need of a cornerback should consider Nelson as a player who can go in right away and rapidly establish himself as a mainstay.
The Green Bay Packers have reportedly released some cap space after letting linebacker De'Vondre Campbell go. Nelson might be a wise addition to the CB room for the squad.
Eric Stokes hasn't cemented his position as the Packers' starting cornerback yet, so the chance to be the CB2 behind Jaire Alexander might still be open.
4) Donovan Smith, offensive tackle
Donovan Smith has won Super Bowl rings with both the Tampa Bay Buccaneers and the Kansas City Chiefs while protecting two of the best quarterbacks in league history, Tom Brady and Patrick Mahomes. Smith is 30 years old, has a solid injury history and most likely still has a few more good seasons left in him.
5) Ryan Tannehill, quarterback
Although Ryan Tannehill has never been a quarterback of the highest caliber, his athleticism has allowed him to play at a high level in stretches. Though it's unlikely that he will relive the magic he showed in 2019 when he was named for the Pro Bowl, the veteran is the finest possible fallback option in case a team needs a quarterback.
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