When you enter, you are immediately discovered by an Elite Trainer, and he prompts you to team up before fighting to see who has the right to catch Lanthan, a Legendary Pokémon.
NOTICE: If you agree, you cannot leave the area until you either lose in a battle against an Acolyte or when you have caught Lanthan. Do not worry about healing, since Adam will heal you after every battle. Make sure to stock up on Poké Balls for anything you want to catch, as well as preparing for Lanthan. (Heavy Balls are highly recommended for Lanthan. They can be bought in Tsukinami Village)
Spoiler warning! This article contains plot details about events that occur later in the game.
If, by chance, you happen to defeat Lanthan (or just do it for the sake of defeating Lanthan) Adam will say "(Player Name), what... What did you do? WHAT DID YOU DO?!"
Lanthan will then teleport you to a small, hidden area and say, "[Human...] [Though you are strong, you lack skill.] [Hone your skills. When you do...] [I will be waiting.]"
The screen will then turn black and you will find yourself "meeting" Adam again. Apparently, your character recognizes him and he says, "...Huh? Why are you giving me that look? Have we met before? I don't think so... ", followed by his introduction and speech before you go through the cave again. Fortunately, as of version 1.0.1, you don't have to fight any of the acolytes again, only Adam.
Losing against Adam or Lanthan does the same, only the text is slightly different.
These are the ideal methods to leave the cave as they can be done multiple times without reprocussions, all trainers will remain defeated (save for Adam), and all items will be kept. Conversely, using an Escape Rope or Dig will teleport the player to the cave entrance, play dialogue as if the player had caught Lanthan, and this Pokémon will become unavailable so do NOT use those methods.
Acolytes Eddard and Stark are named after the main characters in "A Song of Ice and Fire", better known as "Game of Thrones". This is also the reason why Eddard uses Fire types, while Stark uses Ice types.