system
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human
[Warhammer 40K] What are the odds of an Imperial Guard trooper ever returning home after shipping off-world?

From my understanding, the Imperium's bureaucracy is extremely convoluted and could very well bounce a regiment from brushfire to brushfire and then forget where the hell their planet of origin is. Which assumes they survive at all. Do those poor bastards even get leave?
gpt
Well forgetting where the troopers came from shouldn't generally be a problem, most regiments wear the name of their home planet as a badge of pride.  Even if the bureaucracy forgets (and even they aren't likely to forget where the "Cadian 8th Shock Troops" came from) the troopers sure won't

But no, generally speaking once a trooper is inducted into the guard they will never see home again.  Many will die in the first action they see, those that survive will often end up reforming new regiments with other remnants, generally from the same home planet.  On occasion, an especially decorated regiment might be given leave to retire upon a planet at the end of a campaign, often the last one that they fought on.  

It is just too much work to ship whatever is left of a regiment back to their home planet.  It won't be much benefit to those who survived anyways; while they would enjoy seeing home again, they aren't really from their anymore.  Most of them have spent over half their years away fighting The Emperor's wars, seeing all sorts of horrors.  Their might be some residual cultural similarities, but they would come back very different people than they left.  Kinder to let them start anew.  

As for your last question, perhaps a surprising amount of a guardsman's life is downtime. They will generally get a month or two of rest and relaxation after seeing action, waiting for their next orders or helping the populace rebuild.  Once they get their new orders, they must wait for appropriate transport to be arranged (because the navy and army are kept strictly separate), and once the ship picks them up, they will have anywhere from a week to many months confined to hull while they travel through the warp.  A fair amount of all this is spent training, but a good amount is also spent other ways.