So I found what happens when you make a Covenant with the End of the Cycle and it decides to collect on your debt to it...
When you first make a covenant on it, you will gain a +100% production bonus on everything: Unity, Influence, Science, Research speed etc.
In exchange, all of your planets are now Shroud-marked - Something bad is going to happen to these worlds at some point in the future.
But, after those 50 years are up, every single planet you own will become a shrouded planet and every pop on them will die, all your stations will be destroyed, your megastructures will become derelict, all your fleets will become ghost ships, you will lose 50,000 minerals, energy credits, influence and unity and all your territory will be lost.
But!
It is not the End just yet. Some of your species will manage to survive as they foresaw it all coming and flee to a planet named Exile and you will be given 1K resources to rebuild your empire. However, the End of the Cycle is not done with your galaxy. Your species' sacrifice will summon a powerful Psionic entity above your former Homeworld simply named "The Reckoning", a massive entity that is larger than the Sun, and it is the spawn of your species' psionic might - it is also the most powerful single entity in the game and it will roam the Galaxy, purging it all of life.
Unless you stop it.