In reply to GhostProtocol.

It can go one of two ways. If a player is released from their rookie deal and clears waivers then that contract vanishes. They start fresh with a new deal with their new team, or perhaps a new deal with the same team if they were cut and put on the practice squad (e.g. Cedrick Wilson in 2019).

If the cut player is claimed off waivers then his rookie contract stays intact with the next team. We saw this last week when Carolina claimed Jalen Jelks after Dallas released him. He's under contract with them until 2022, now, just like if he'd stayed with the Cowboys.