Note: In this answer, I will be quoting from PARANOIA 2nd Edition and PARANOIA XP. I think the advice here may still be applicable to the new edition, especially because very little in PARANOIA depends on the rules of the game. I am an experienced GM, having ran PARANOIA XP missions since the 2000s.
First, let's deal with the published missions.
I suspect that most PARANOIA missions are written with the assumption of being one-shots, hence the terminal endings to serve as a nice, memorable bookend for characters.
But that does not mean that you must always run one-shots. You just have to modify the missions and change the endings to be less lethal and to imply that players are impacting the larger plot in some shape or fashion.
Modifying the published missions was actually encouraged in both 1st Edition and 2nd Edition. For example, 2nd Edition wrote:
You can always take a published adventure, use its basic structure or premise, then twist it in whatever direction you like. There are no Game Design Police who will come to your home to make sure you run an adventure the way it was published. In fact, for Paranoia, this is our recommended method - use the published adventure for structure and inspiration, then create and improvise to your heart's content.
I have done that before for a few missions, where I liked most of the content, but not all of it (like, say, the hosejob endings). It's rather empowering, really.
However, even when you modify a mission to be less lethal, players may still die. What then? Here's a quote from a passage from the PARANOIA XP rulebook
about running PARANOIA campaigns:
[W]hat about the fatality rate? Easy: Treat the players themselves as the continuing characters. A player has one Troubleshooter now; he’ll have another next time; so what? Let all his characters know what he knows. Let the player carry his knowledge of deathtraps and proper conduct forward from one Troubleshooter to the next. Is that any more implausible than the whole identical-clone-backups device?
In PARANOIA, unlike a lot of other (non-fun) RPGs, many players regard their characters not as roles to play but as mere puppets or placeholders. This is fine—in fact, it may be the best way to play. The Computer requires all Alpha Complex citizens to think and behave pretty much alike. So regardless of his PC’s specific background, a player has ample rationale to just play the character as if he himself, the player, were there in the briefing rooms and corridors, doing what he himself would do. This works out well, as long as the player feels the fear and insanity of the setting.
Then, too, there are ways to keep even individual Troubleshooters alive. Under the Straight rules for treason accusation and clone backups, experienced and careful players can keep their characters around long enough to reach decently high clearances. At that level the nature of the game shifts to a less immediately deadly form.
This is a question about PARANOIA Rebooted, not about PARANOIA XP, so here's the basic gist of those rules so you can convert them to PARANOIA Rebooted if you think you need to do so:
- The "Straight rules for treason accusations" boil down to requiring more evidence before convicting somebody and reducing the punishment for treason down to more reasonable levels (so, maybe 1-2 treason stars for a minor offense)...
- The "Straight rules for clone backups" boil down to allowing players purchase new clone backups. Though players may get themselves in debt (and may dig themselves even deeper into debt if they want to 'clean' their genetic template), at least they get to live longer past the 6-clone limit. Note that if players go too deep into debt, The Computer may erase their clone template as punishment.
Basically, just dial down the lethal nature of the game and allow players to purchase new clones in case they get close to running out.
Is there some sort of Last-Will-And-Testament system that can be used to pass on XP Points and/or loot and/or information between adventures?
As mentioned in the PARANOIA XP's quote, it's perfectly fine to pass on information to your next character. However, I would tell the player that such information would be considered "rumors"...and rumors are treasonous (so don't get caught knowing it).
So, the question turns to passing on XP Points and loot...
In PARANOIA XP, you had Perversity Points (a meta-currency that players earn for being entertaining and can spend to boost character success). Perversity Points belong to the player (not the character), so if a character loses all their clones, no sweat, the player still keep their Perversity Points and can use them when running their new character.
Paranoia Rebooted doesn't have Perversity Points anymore, and it may be weird to treat XP as a kind-of-Perversity since they have in-game fluff and technically belong to the character. But...
Since the GM can still award players XP for being entertaining (through the Achievements system), I'd say you can just have players inherit the XP of their previous character. You can probably rationalize it by saying to the unlucky player as he writes up a new character sheet:
"Yes, The Computer tried to vent the excess XP Points to the Underplex. Emphasis on tried. Your secret society have secretly recovered the XP Points, and gave them to your new character as a reward for their previous treasonous activities. Don't mention this to anybody though, or The Computer will ask some interesting questions."
Alternatively, you could just boost the security clearance of the new character, as okeefe suggested in his answer to running a PARANOIA campaign using PARANOIA Rebooted rules.
Doing so means you don't need to trot out a transparently bogus rationalization to justify why the player still retains their XP Points, while still boosting the player well-enough to compensate for his loss of XP Points (especially since the only way to get a security clearance promotion is by...spending XP Points).
Last, items. I wouldn't allow items to be carried over (but I don't really have a good reason why - I suppose I think carrying over information and meta-currency tends to be good enough for a new character, and it makes more sense for items to be unrecoverable). If you want items to be carried over though, use the same excuse I did for justifying how a new character recovered XP Points.
Additional Reading: okeefe's answer
to "How can I run an ongoing Paranoia campaign?" (answer also addresses how to run campaigns using PARANOIA Rebooted)