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In their first appearances, they were described as unable to survive long without a host (or just unable to breathe on Earth without a host, depending on which writer you asked). That aspect was quickly retconned/forgotten by later writers.
The Daemonites on Earth were mostly fanatical freedom-fighter/terrorist types who would do anything to defeat the Kherubim. The ones seen on Khera in the later WildC.A.T.S. series were downtrodden third-class citizens (below even the Titanthrops) confined to segregated ghettos and reservations. Their home planet was described as mired in postwar poverty, and kept that way deliberately for thousands of years after the war by the Kherubim victors.
The New 52
After the Flashpoint, the Daemonites were an ancient species that were created by the Kherubim as a servitor race who rebelled against them. At some point, they attempted to harness a great source of energy only for them to accidently release the Gravity Miners to their universe. These extradimensional alies were responsible for devastating the Daemonite home galaxy long ago. Within the empire, a powerful Daemonite by the name of Helspont rose ot power with his god-like metahuman abilities. However, his species would come to fear him and ultimately were responsible for imprisoning him. By this era, the Daemonites had reached the limit of their evolutionary ability and sought a new homeworld as dictated by their prophecy which they believed would bring about their survival. One of their enemies was the Thanagarians who managed to repell their efforts. This saw the them engage in diplomatic negotiations with the Thanagarians but this was to secretly to unleash a bioweapon that decimated their population, removed their wings and killed their king. At the same time, the Daemonites arrived on Earth where they secretly began infiltrating the populace.