What would happen if a Gods of Destruction fuse together?

[Hellspawn28]

If two Gods of Destructions fuse with the potara, what would happen to the Kaioshin as well? Would they also fuse too? Also if Beerus and Champa fused together and if someone like Shin died, what would happen to the fusion?

[Pantalones]

I don't think two Gods of Destruction fusing would cause two Kaioshin from their respective universes to fuse along with them (their link is only "if one dies so does the other," other things besides death don't transfer -- otherwise Beerus might've accidentally sealed himself along with the old Kaioshin!)

But if one of the fused gods had their Kaioshin counterpart(s) killed off while they were fused, I figure the fusion would either become unstable like Merged Zamasu or they would defuse right away.

[GreatSaiyaman123]

Nothing, i think. Comparing in a smaller scale, Piccolo merged with Nail and powered up, but nothing happened to Kami. The fusion would not be a Haikaishin though, considering it's a brand new being who isn't either of the fusers.
As for the fusion dying, the Kaioshin would be just fine. The fusion wouldn't be a Haikaishin just because his fusers were, after all. Kamiccolo wasn't a god when he fused with Kami.

[Speedster]

Potara fusion is an addition. A 1+1. Not a 0.5+0.5 like a child from parents. If you fuse with somebody else you continue to exist as a whole – just it happens that you become a part of a combined character that is the sum of parts. U7 Kaioshin fused with Kibito and nothing happened to Beerus as Kaioshin continued to live on as part of Kibitoshin. Similarly, if a GoD were to fuse with anyone (including another GoD) the Kaioshin would be unaffected as the GoD they are associated with would continue to live as a part of a fused character.

[Pantalones]

The fusion wouldn't be a Haikaishin just because his fusers were, after all. Kamiccolo wasn't a god when he fused with Kami.

That was Namekian fusion, though, not Potara. Namekian fusion doesn't really create a whole new individual the way other forms of fusion do (notice that Piccolo's appearance doesn't change at all when he fuses with either Nail or Kami... he didn't get a "middle-aged" look combining his youth and Kami's age or anything like that), it's almost closer to an absorption in most ways. Piccolo was the "base" of the fusion because they needed a powerful fighter, which meant that "Kamiccolo" was basically just a power-up for Piccolo (along with him gaining Kami's knowledge and maybe some personality bits, just like what happened with Nail.) If they had decided to go with Kami as the "base," it would be the other way around and presumably would still be God of Earth afterward, since it would be Kami gaining a boost in power and Piccolo's fighting skills and such rather than actually becoming a new person.

Now, if there was a Namekian God of Destruction who fused with another Namekian and the other non-godly Namekian was the "base" for the fusion for whatever reason, then yeah, the resulting Namekian wouldn't officially be a God of Destruction -- even though they'd probably have the power of one.

[Cetra]

If you fuse with somebody else you continue to exist as a whole – just it happens that you become a part of a combined character that is the sum of parts.

That's not really true. The show is always very foggy about it either being the destruction of the original consciousnesses through them being the component of a new one or instead just being a collective consciousness. And most of the time it leans towards the new person thing. You cannot really count Piccolo because it is entirely different. And even for the Kaioshin it was never established whether he just treated himself that way because of the memories or not. It was one of the things that was not consistent with other things.

[Galan007]

If two Gods of Destructions fuse with the potara, what would happen to the Kaioshin as well? Would they also fuse too? Also if Beerus and Champa fused together and if someone like Shin died, what would happen to the fusion?

The Kaioshin would remain individual, imo. As mentioned, they are only linked to the Destroyers by death -- aside from that, what happens to one does not happen to the other.

If one of the Kaioshin were killed, however, I'd imagine the Destroyer-fusion would swiftly destabilize/split.