Let's say we have a certain Trill symbiont with a host. What would happen if the symbiont was duplicated under the condition that:
- The host and symbiont were transporter cloned. (2 Jadzia Daxs)
- A person from an alternate timeline with the same symbiont ends up permanently marooned in the prime timeline. (Larry Dax from a timeline where Curzon didn't reinstate Jadzia coexisting with prime Jadzia)
- A past host comes back from the dead with a version of the symbiont a la Spock or Shaxs, or even something similar to Doctor Who's concept of an extraction chamber (Jadzia got bored in Sto'Vo'Kor and decided to climb the Black Mountain, meaning her and Ezri exist simultaneously)
I imagine in all of them, the commission would at least let the duplicate live for the rest of the lifespan of the original host, much like the Federation at large treats transporter clones.
However, what happens when it comes time for the symbiont to be transferred? I can't imagine the commission's ideology would smile upon duplicate experiences under much of the same rationale against re-association: there would be a duplication of experiences rather than the acquiring of new ones.
I think in the first case at least, it is reasonable to assume that they'd begrudgingly transfer both symbionts, as both have the equally valid claim to being the original and randomly killing one is straight-up murder, which I imagine the rest of the Federation would dislike.
They might also do so in the second case, as at least our Larry boy has some different experiences even if some are duplicate with prime Dax.
The third one is where it gets very muddy. The nature of souls in general is a muddy subject - twofold when there are two beings involved. For the sake of argument, we'll say the Jadzia in Ezri's symbiont accessible by Zhian'tara is a "backup" of Jadzia up to her death and that a separate Jadzia Dax went to Sto'Vo'Kor^1^. What then?
1: I make this assumption because a) Ezri doesn't have Jadzia's memories of Sto'Vo'Kor and b) it was the combination of Dax and Jadzia that engaged in Klingon ritual and "just" Jadzia would not be the person that participated. Of course, this starts getting into the more mystical parts of the franchise, and it's probably good they keep it vague even through it makes canon discussion like this a nightmare... a FUN nightmare.
I've always considered the symbiont to be like a brain extension that while attached allows the host to access all the memories. Sort of like a flash drive adding storage to a computer. Even if the initial computer crashes the flash drive can still be plugged into a new machine and the files recovered. And, an unjoined trill (like what happened to Jadzia in Invasive Procedures can only remember what was recently accessed in the symbiont from her own brain (like a data cache).
If we are dealing with Thomas Riker or William Boimler Logic, I would say that you now have Jadzia 1 and Jadzia 2 and each is their own Dax as well.
In case number 2, I would say that most likely, as long as parallel Dax is compatible with Prime Trills, you'd still be able to pass it along to the next person. I have a feeling that the Dax's might argue about who deserves what though. That would be/have been an interesting episode.
And as long as I am writing fan fiction, it would be interesting if Dax got some sort of worm concussion and lost certain parts of its memory. Could anything be done? Is it the same Dax without the memories of Curzon? Can we travel to an alternate timeline or back to the past to get a close approximation of the Curzon memories and somehow do a Young Frankenstein brain transfer to set everything right? Also the B story is Quark and Dr. Bashir having love triangle problems with alternate Dax or whatever.