I'm not denying the soft clone is identical to you in every conceivable and possible way, right down to every brain cell, save for the gap in memory.
What I'm saying is that it is the instance of the clone that dies, does die. You die, and the clone wakes up. You could wake up ten of them at the same time and they all have individual consciousness. There is no shared memory and they each have their own experiences, ie they are separate people starting with the same recipe. If you kill one the other's don't feel it, and the one you killed, is dead.
The idea of self and identity is fragile like this. If I had a soft-clone backed up a week ago and got shot today, only to wake up tomorrow missing a week and a day and being told what happened, I would likely have problems thinking that this is what happened to "me".
"Pictures of GTFO" can be the same as "I can't remember, so it did not happen to me." A falasity, sure, but one that seems logical from that point of view. The guy who got shot yesterday was not me. I would have done all these things all week but got myself offed. Now I got to find the guy who wanted me dead, deal with him, and do what I was supposed to do this week. This set-back is annoying; I have better things to do.
So long as only ONE instance of you are active at a time, it's "you". There are no other entities like you. Plenty of other humans yeah, but none of them are "you". This is easy to see in your unique physical traits (though these can be copied) and your unique "soul" (all the info pertained within can be copied as well; it is - your clones and their back-ups.)
The very instant more than one instance of this back-up goes live you have a major issue and likely a freak-out crisis-of-personality-and-identity moment coming up. Your not unique anymore. Arguably if someone simply took samples of your DNA and managed to grow a physical clone of your flesh, things would still be ok - they would not have your mentality nor your memories, and are thus only a collection of look-alike copies, in the literal sense. The moment a complete copy, with your exact physical and mental traits hammered down to the last nail arrives, however?
Both of you will either think your the original and the opposite is the needless extra, or both of you will come to think and really take-in the idea that the person you USED to be is dead, and your both copies of the same person. Both can't have the assets, both can't have the name and ID-card or the originals social connections, so this alone will warrant issues. This is exactly why CONCORD forbids multi-clone activities for capsuleers - not becasue it can't be done, but for the shit-storm of social and legal issues that would ensue.
So long as it's one active, and in worst cases, only one spare that's activated most capsuleers are likely to have no problems with this arrangement. So they got shot in a station, big deal. Minor set-back equal to whatever time passed from last back-up to now. They pick up where they left off, likely update themselves in whatever manner they wish and move on with their lives as of nothing happened.
If the soft-clone's pile of meat that resumes after the original's clinical death is a fresh person or effectively the original person who has 'slept' since the last backup is likely an unsolvable question of ethics, physics and psychology as far as RL arguments are concerned.
And this should likely be split to a new topic, I'd do it but I'm positive I don't have the needed permissions to do that, etc.