Even in a perfect world, if all validators are thoroughly vetted and all validators are honest, there still may exist more than a single chain at any moment (different validators create different blocks). In such a scenario, both forks will continue to validate blocks and add new blocks. This process lasts until one of the chains validates a block before the other chain completes and becomes the longest chain. At that point the longest chain becomes the accepted chain and transactions mined on the shorter chain are rejected (it is possible that the transactions rejected on the shorter chain might have been included in other blocks on the longest chain).