I've had a couple players claimed off revocable waivers after the trade deadline. It was the same team that claimed them. They weren't designated for assignment. The team that put that claim on them never submitted a trade offer. What happens to these players after the season is over? Do they go to the team that claimed them? Or is it just a trade offer deal? Hope I didn't mess this up.

Are they still on your 40 man roster?

Yes they are. On my ML roster

Then nothing happens. They'll be on your BL roster after rollover.

Waivers before deadline:

If someone claims, that team acquires player immediately

Waivers after deadline:
If team automatically revokes-
If someone claims, you keep your player but the claiming team has "trade exclusivity". In other words, you must either keep your player for the remainder of the season OR you can only trade the player to that specific team. Nothing special happens at the end of the season; if they are under contract for further seasons then they remain under contract, and if they expire at the end of the season then the normal free agency scenario applies. Similarly, if they are still within arbitration period then the normal arbitration schedule applies. This is standard and nothing to be worried about

If team does NOT revoke-
If someone claims, that team acquires player immediately

Ok thanks..