When a player is released by his MLB team, he remains available in his most recent league type in BBM. MLB-released players will never be deleted from their BBM leagues. In MLB, when a team releases a player, it is still responsible for that player’s contract.
Note: This rule applies even if the player is placed on waivers, a team from the other league makes a waiver claim, and the two teams complete a cash-only waivers deal. This is classified as a waivers transaction by MLB, not a trade.