Your train is best suited for your dominoes. Early on, you almost certainly want to close your train as quickly as possible. But if you're just stuck, or it's late in the game, you may have no choice. To close your train and prevent others from playing tiles on it, you need to lay a tile on your own caboose. Playing on a public train domino or some other player's doesn't enable you or anyone else to close a train with the remaining dominoes. You can only close it by playing your own tile on your own train.