Later, about halfway through the game a dungeon called the Ancient Cave becomes available. You can't take anything with you inside unless you found it in a blue chest inside, and all of your party starts at Lv1 (Capsule monsters included) for the duration of each trip (whether you die and get kicked out, or find the Providence item)
Fun fact about the Ancient Cave: Anything found in blue chests OUTSIDE of the Ancient cave can be brought in with you, so keep all of your Blue Chest gear and don't feed it to a CM, or sell it as you can give yourself a head start on getting some nice gear from the cave to use in the rest of the story.