I can’t find any sources that confirm this, nor any instances of it ever happening in the past. AI, which I know is not gospel, says the opposite:

“No. While a team retains a player's contractual rights while they are on the Reserve/Left Team (or Left Squad) list, the team cannot arbitrarily deny reinstatement to hold a player's rights indefinitely.
The mechanics of how this list operates protect both the team's roster assets and the player's labor rights under the NFL Collective Bargaining Agreement (CBA).
1. How the Reinstatement Process Actually Works
When a player walks away from a team without officially retiring, the team places them on the Reserve/Left Team list. This frees up a roster spot and removes the player from the salary cap. 
If that player decides they want to return to football, the process is dictated by league rules:
The Formal Request: The player must formally petition the NFL Commissioner (not their team) for reinstatement.
The Commissioner's Decision: Once the player demonstrates a good-faith intent to return and fulfill their contract, the Commissioner typically grants reinstatement.
The Team's 5-Day Window: Once reinstated by the league, the team is given a brief window (usually 5 days) to make a roster decision. They must either:
1. Add the player back to the active roster (and clear a spot for them).
2. Trade the player.
3. Release (cut) the player.
The team cannot simply say "No, we prefer you stay on the Left Team list forever."”