Paper-Version: Paper version git-Paper-691 (MC: 1.16.5) (Implementing API version 1.16.5-R0.1-SNAPSHOT)

CraftBook_3.10.4-Build4700.jar

We have set up with Craftbook so that the users get a Minecart when they click on a rail and it is automatically removed when they get up.
That works very well in the game.

Now the problem:
You click on the rail and you sit in a minecart.
If you log out and log in again you can dismantle the minecart and it is yours. It will then no longer be drawn in by the plugin

This sounds like something else causing the issue. The carts are in no way tied to a player's login status, no data is stored on the player, only the minecart.

Either way - this mechanic has been ported to CraftBook 5 and is no longer supported on CraftBook 3.