The remnant spirits are the small part of a powerful entity's spirit that was left behind in their [Treasure Lands] or the [God Ruins] to look after them.
Even though they were part of their own spirit, those powerful entities fear that their remnant spirit gains their own consciousness by some external factors.
Once that happens, they would try to return to the main body and slowly take control of the body while replacing the main spirit.
Therefore, those powerful entities leave behind a set of rules for the remnant spirits and one of those rules was not killing the participants entering the [Treasure Land].
The moment they kill the participants with their own hands, the remnant spirit also disappears into the void.
<I am prepared to die along with you. So, if you tell me what you are hiding, we both can live>