I believe that Ultra Space is not a complete universe of its own, but an inchoate and incomplete fragment of spacetime, hence its repeated incursions into the Pokemon world.
Lillie says that the air of Ultra Space 'hurts to breathe'. Since it appears to contain no plants of any kind, I would assume the air is saturated with carbon dioxide. If this is true, Ultra Space cannot have a self-sustaining ecosystem, but instead relies on periodic influxes of fresh air from the Pokemon world. This would also mean that the Ultra Beasts did not originate from Ultra Space, but are instead descended from Poke-world Pokemon that fell through Ultra Wormholes.