Split slimepeople are NOT player controlled, but rather the original slime person can swap between the two mobs at will. If one of the slimepeople should die under player control, the player won't be able to swap back to their living body.
Splitting only creates a new body, any items you have on you are not duplicated.
In testing this takes longer to achieve than you might think, even under ideal "FOOD EVERYWHERE" conditions it can take nearly 10 minutes to produce a split slimeperson. The initial slimeperson is also apt to get fat if they try to do this more than once.
Slimepeople now take half damage from sources of heat, but double damage from sources of cold.
Incoming
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