Do monsters stay spawned after you complete the objective for each room, and open the door to the next room?

Example: I entered the Trash heap room, which has 2 shadow dragons and 4 search tokens.

You have to successfully pass attribute test to search. Once all 4 tokens are uncovered, you discard that exploration card.

So I killed the minion shadow dragon, and uncovered the 4 search tokens, and opened the door to the next room --- Does the remaining shadow dragon just despawn once the exploration card is discarded (or when a new exploration card is drawn) or does he stay until he is killed?

Would a monster keep following you through each room until they are killed (or respawned by opening a room).

From my many times playing this co-op game, the only time monsters despawn is when you need to spawn them in the new room.

So for this instance, since the new room didn't require you to spawn more shadow dragons. The old ones will continue to chase you until they're required for new rooms.

I've had this happen several times with zombies chasing the heroes as they move on.