Perhaps one of the most interesting quotes in this respect is from "Infinite Regress":
EMH: "During your time with the Borg, the Collective assimilated hundreds of different species. All of those neural patterns were integrated into the Hive Mind."
7of9: "Of course."
EMH: "That means they're in your mind too, stored within your cortical implants. Dormant until now."
The Doc's "all of those" is probably exaggeration, and Seven doesn't accommodate the sum total of Borg knowledge in her body - but we know she accommodates a lot. One wonders if all personalities are stored in as complete a form as the ones that surfaced through Seven in that episode, or if those thirteen were merely specifically preserved examples of each species.
Odds clearly are, though, that the physical deaths of those thirteen would not mean the end of their lives, if any random Borg (or at the very least the ones separated from the Collective at the time of the physical deaths) can store their consciousnesses or personalities in such detail.
Since the personalities remain in the original individuals, at least in some state of dormancy (like the Seven and Locutus examples indicate), I agree that we must start speaking in more multifaceted terms, or at least accept complexity when using simple terminology, in all things dealing with "self". At least when the self in question has been assimilated...