In the 1.8 update, Awakened Fallen Empires have a 'decadence' meter that starts filling up some time after they awaken (the stronger they grow, the faster it goes up). It weakens their economy and fleets and makes their subjects far more rebellious, and has very severe effects at high levels of decadence. It should mean that you can swear fealty and try to outlast and overthrow them if they're simply too strong to fight head-on. They'll also prefer to force empires into subjecthood rather than annex them outright (though they'll still likely grab a few planets to punish you for not accepting peacefully).