Off-the-wall suggestion:
During the Byzantine-Persian War, Egypt falls into revolt under a local figure/commander who effectively exploits religious differences to spark uprisings up and down the Nile, leaving loyalist Byzantine garrisons isolated. Said garrisons eventually surrender, defect, or are destroyed.
Constantinople would respond more quickly, but the Sassanids have been making great victories and rapidly advancing to the Levant and Anatolia. The new Principality of Egypt offers a separate peace with the Persians, and they accept. Egypt also begins negotiations with Constantinople, continuing to supply critical grain for a truce.
Ultimately, Heraclitus attains costly victories against the Sassanids and begins recovering Anatolia and the Levant, even advancing into Mesopotamia. Egypt changes tactics toward suggesting that maybe being an autonomous vassal of the Emperor, personally, might not be so bad. This of course has nothing to do with the dramatic shift in power back toward Constantinople, and the fact that the Emperor is no longer quite bereft of military force, nothing at all, surely.
Regardless, the offer is more or less accepted--returning Egypt back to the Imperial fold, but closely tied to the Emperor personally, which is not entirely unhelpful in giving the leader of the Second Rome more than a little leverage against troublesome nobility or potential rogue commanders.
Unfortunately for this nice arrangement, the Arabs unite under a charismatic leader and burst into the middle east. Mesopotamia is quickly taken, and the Levant barely holds thanks to Egypt's own undevastated military potential. Persia itself soon falls, but the momentum of conquest ebbs before the Levant and Anatolia are overwhelmed, though they do suffer yet another round of destruction through raids, pillaging, and army foraging.
In the end, the Empire of the Romans survives the storm, barely. And an independently-minded Egypt has a new external reason to consider the value of Imperial cooperation.
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Probably implausible.