My uneducated guess would be:
1. Since eternum basically is a form of astral projection, the inferior part of the split being, i.e the part mostly existing in eternum would warp to where the real body is, since eternum, despite being of many worlds, is in its own plane of existence and thus the two pieces would fuse.
This would imply though that the visors and clothing they wear would also morph into whatever clothing they had in-game or disappear or get left behind since it works in different laws thus since eternum basically operates on different laws, depending on how heavy the penalty to the balance of the universe is to such stupid actions, abilities and clothing may or may not continue to function as they did normally.
2. The second is just that bringing you from outside while in-game would just lead to you looking at a sleeping beauty version of you, nothing more