"If he dies, he dies."
Um ... I mean, Greetings and Salutations. With the exception of demons (and I believe all true supernatural beings) when they die they die. Ever since R:UE (I think it started there, then again in Hades) demons (and I believe other supernatural beings) will (eventually) revive in their home dimension. Those are specific exceptions (the benefit of being a demon or other supernatural being, not something everyone gets). Otherwise death means dead, and not sure why someone would suspect otherwise. If death meant reincarnation there wouldn't be much harm in fighting to the death or committing suicide (which is something a summoned being will not do, but why wouldn't it if all that would happen is it comes back to life at its home?).
As for the spell version returning it home when it dies, that would be debatable. I can find wording suggesting it may do that ("the creature will remain in this dimension until the mission is completed or it is slain"), but I would in general think not (by everything else that is written, not the single line). With the spell, there is no set duration (at least the ones I've seen from other dimensions, not counting the ones that simply summon something within range of the spell like the animal ones). For example, the Shadow Beast one lists two minutes, three hours, or until the mission is finished (depending on the task and situation). After it is completed, the summoned may still not return to its home dimension. So it seems it needs to want to return home (and it can't want to return home if it is dead). Note: This is all taken from the write-up of the spell (unless it was drastically rewritten in R:UE).
Now, with what will happen to it after it completes its mission and is still alive, from what I can find (with the Shifter), the Shifter would have to be able to send it back (which may require force/control as it states most other dimensional beings will LIKE being here). I specify with a "Shifter" because PF has a Summoner, and with the Summoner it seems like the being can return home when released or it breaks free or resists control. However, the rules for a Summoner are quite different. However, a Shifter follows quite a few different rules. With a Shifter, it only arrives in this world if the Shifter brings it or the contacted being forces its way through the Communication Rift. There is talk of the summoned attacking the Shifter or running for a door or window, but there is notably no mention of it just returning home. For example, if the Shifter beats the being in a physical confrontation, it will be willing to make a pact in favor of death (not just sneaking off home by mystical means). Unless it can dimensional teleport, it looks like it stays until someone sends it home (or it finds a random rift).
These are the answers as best as I can find them. I can bring out exact quotes if necessary, but tried to convey the general references. Though if for some reasons this is disagreed with and requesting more references, perhaps some references to suggest otherwise would be nice (as opposed to just refusing the answers given). I suppose I just don't see where the line of thought is really coming from (but I could just be missing references which is why I'd like to see them). Of course, I'm always open to creative G.M. rulings if there is a good reason, and they're welcome to do what they'd like in their games. Hopefully none of that came off badly, critical, or hostile (none of it was intended as such I assure you). Thank you for your time and patience, please have a nice day. Farewell and safe journeys.