He did that, Jygg did that, so that he could finally go into retirement, from what I have read, it sounds like he doesn't die, in every possible way.

A few things run through each other here.

Daedra can only enter Mundus when summoned or on a special occasion. The Aldudagga outlined one of those special occasions as Dagon could enter when allot of destruction was going on. I don't think their birthday/summoning days are included in this as well, they have to be summoned. The other limitation in effect is Sotha Sil's pact, limiting summonings to experienced conjurers, which may or may not be in effect.

Maybe the CoC becomes an avatar of Sheoggy - and retains enough of his own nature not to be bound as a full Daedric Prince. So if part of Sheoggy is in the CoC then only part is in Jygg soo neither part of Sheoggy is totally bound by normal conventions pertaining to Daedric Princes. Thus I would imagine that Sheoggy can now influence Jygg and in doing so turn Jygg from an absolute into a non-absolute and therefore no longer so infinite in his normality.

This raises the interesting possibility that Jygg is also no longer a true Daedric Prince ...

And so it may be that the CoC has thereby been tricked into letting both Sheoggy and Jygg loose to roam the mortal plane(t) = interesting times ahead