It's not quite as simple as Raiders have first choice on any player who gets cut or waived.
Here's excerpts that explain the process from (paywall) link to an article in The Athletic:
https://www.nytimes.com/athletic/754326 ... explained/
Waived vs. released
Whether a player is waived or released comes down to how much experience he has accrued in the NFL.
Veteran players who have at least four accrued seasons are outright released. They instantly become free agents and can sign with any team. In some cases, they might even return to their own team after further post-cutdown day moves are made.
The NFL defines an accrued season as spending at least six games on a team’s 53-man roster, physically unable to perform list or injured reserve.
Players who are cut and have fewer than four years of NFL experience are subject to waivers. These are players who, based on their experience, would have been restricted free agents or exclusive-rights free agents in the prior offseason’s free agency. After a team waives them, they have to go through the waiver wire.
Typically, the waiver wire process is 24 hours, but on cutdown day, it’s slightly shorter.
Although teams began making cuts in the days leading up to the deadline, those moves aren’t official until 6 p.m. ET Sunday. Teams have until 1 p.m. ET Monday to put in claims.
If a team claims a player off waivers, it inherits that player’s current contract.
If a player clears waivers, he becomes a free agent and can sign with any team, including the practice squad of the team that cut him. Teams can typically sign 16 players to the practice squad. A 17th player can be added if he’s part of the league’s International Player Pathway program.
Last year, 29 players were claimed off waivers on cutdown day, with the Tennessee Titans, who were at the top of the order, picking up four players. In 2024, 27 players were claimed off waivers on cutdown day, with the Carolina Panthers, who were at the top of the order, leading the way by picking up six players. The Las Vegas Raiders top the claim order this year.
What happens when a player is claimed?
Each team must have its roster trimmed to 53 players by 6 p.m. ET Sunday. If a team trimmed its roster to fewer than 53 players and claims a player waived by another team by Monday’s deadline, it must make a corresponding move to keep its roster in compliance.
Teams that claim a player must make room for that player on their 53-man roster; teams cannot claim a player and place him directly on their practice squad. The player would need to clear waivers and become a free agent to join the practice squad.
Many teams go through this period without gaining a single player off waivers, or even without submitting a waiver claim. However, some teams choose to tinker with their roster through the waiver wire, which is why Sunday’s roster deadline isn’t always the best indicator of each team’s 53-man roster across the league.
What if multiple teams submit a claim on the same player?
The waiver claim order is fairly straightforward. Throughout the preseason and the first three weeks of the regular season, the waiver wire order is based on that year’s original NFL Draft order (meaning trades and forfeited picks are not relevant). After the first three weeks of the regular season, the waiver order is fluid, based on the standings at the time.
Last year, the Titans had the No. 1 pick, so they had priority to any player waived on cutdown day. This year, the Las Vegas will have the first chance at any player who’s waived. If multiple teams submit a claim on a player, the team higher in the order is awarded the player. Here is this year’s full waiver claim order for cutdown day:
1. Las Vegas Raiders
2. New York Jets
3. Arizona Cardinals
4. Tennessee Titans
5. New York Giants
6. Cleveland Browns
7. Washington Commanders
8. New Orleans Saints
9. Kansas City Chiefs
10. Cincinnati Bengals
11. Miami Dolphins
12. Dallas Cowboys
13. Atlanta Falcons
14. Baltimore Ravens
15. Tampa Bay Buccaneers
16. Indianapolis Colts
17. Detroit Lions
18. Minnesota Vikings
19. Carolina Panthers
20. Green Bay Packers
21. Pittsburgh Steelers
22. Los Angeles Chargers
23. Philadelphia Eagles
24. Jacksonville Jaguars
25. Chicago Bears
26. Buffalo Bills
27. San Francisco 49ers
28. Houston Texans
29. Los Angeles Rams
30. Denver Broncos
31. New England Patriots
32. Seattle Seahawks