An empire is considered homeless if it no longer has a homeworld.  A homeless empire is automatically removed from any existing alliances.  A homeless empire probably will have little direct effect on the game as it continues, but can still play a minor role, since homeless empires can share portal navigation data and ship designs as per usual.  Homeless empires can continue to send messages to other empires with whom they were in message contact. 
 
 
The GM need not wait on orders from an homeless empire in order to processes a turn's order if that turn's deadline has arrived.
 
Note that an homeless empire can still have conquering ships and could possibly retake control of a world.  In this case, the empire would no longer be considered homeless.