The sponsor/ruler's ability to survive the apocalyptic event would be dependent how good they are at political/psychological manipulation/intrigue. I'd say most upper management would survive.
What are your Mad Max skills? If the nuclear apocalypse comes and you survive, what useful skill do you have that will let you continue to live without the rule of law? Can you build a house? Fix a car? Grow crops? Butcher an animal properly? Land an airplane? I've always though everyone should have at least a few of these practical hands-on skills, in case the shit hits the fan. What good are your computer programming skills when there's no more electricity, let alone functional computers? So, you're a social media marketing manager for a global brand? If that's all you know how to do, you'll end up some local warlord's sex slave.
Why would "security forces" listen to some formerly rich corporate CEO? What has he to offer them?
The ones to dominate in groups tend to have social engineering skills, or "Ben Linus skills" you could call them.
They don't need to know how to start a fire, or fire a gun, or fix a car. They can just get other people to do it for them -- not for money, but because they can con them in to it, or exploit their weaknesses, set them against one another, or bribe them with promises.
This is a problem is too small group in a survival situation. A viable group should have the size of a village at least - over 100 people of some diversity.
Otherwise it is very fragile.
Obviously enough resources to start with.
You have a SERIOUSLY optimistic view of the Mad Max type aftermath of a nuclear apocalypse. Fix a car? Land a plane? Those questions imply an assumption on your part that an awful lot of support systems will have survived. (For instance, I'm not at all sure that fuel deliveries would continue to be made after a nuclear apocalypse. I'm even less certain that the electronic systems of most planes and autos will survive the nuclear unpleasantness unaffected.)
Indeed the main item as usual is how to get your army to listen to you. A hard people skill. Logistics is always useful as well.
A trade or skill is a good fallback in case of exile or loss of resources.
Setting aside how loaded that statement sounds, the role in question could easily involve espionage and assassination.
After all, the medieval feudalism did arise in what was essentially a post-apocalypse world.
I know in most apocalyptic movies they aren't around, but it seems likely some of them would be.
Well... one of those is true.
These people are not wealthy by accident. They were not gifted their riches. They have acquired their wealth through pattern recognition, through being right when (almost) everyone else was wrong.
Someone here asked me a few weeks ago why I felt travel might not be so easy in the not-too-distant future - I held my tongue. Not so now.
I spend a lot of time rubbing shoulders with these intelligent, cynical assholes - and while I lack their dizzying material wealth, I find myself having my brains picked frequently on technical solutions for the apocalypse, as I made my much smaller fortune through - you guessed it - pattern recognition. All successful businesses boil down to individuals who can, to some degree or another, predict the future.
Why does this matter? Why am I defending them?
Firstly, I’m not defending their moral worth. Some of these folks are perfectly lovely, others yet you get the feeling are thinking about asset stripping your organs, and set up dead man’s SOS timers before going to a meet, particularly if it isn’t in public.
It matters because they are almost certainly right. This interglacial period is a bug on the windshield of time. This century and a bit of liberal democracy is a mere blip on the radar. These post-war decades of unfettered growth are a fluke, an artifice built on nothing but itself.
Is the planet going to explode, Death Star style? Unlikely.
Is it going to become a place largely hostile to human life? Probably.
You might think that it’ll take a massive event - all-out war, total crop failure, diabolical climate change - but the reality is that it doesn’t take much, and the more interconnected and interdependent our world becomes, the less it takes. We haven’t created resiliency, we have created points of failure. The internet is the ultimate amplifier and feedback loop - information and its impact now spreads and distorts like never before, waves overlapping and interfering constructively and destructively, creating ripples in the fabric of human civilisation. Those amplitudes can only grow so much before said fabric starts to tear, buckle and break before the strain.
No, this is a chaotic system, with multifarious inputs, and a few well (or badly, if you rather) timed shoves will send it way off “normal”.
There are also those who have taken a page from Asimov, and are attempting to hasten the Event, as a crystal of civilisation is more likely to survive a well planned and rapid demolition than a slow, aching, chaotic collapse.
A flood here, a drought there, an insurrection over there, an environmental disaster there, a refugee crisis here, a small food shortage, an interruption to power supplies, a market crash there, a bread riot here, a mass exodus here, a closed border there, martial law here, panic there, sell-offs here, no economy here, no food here, no security here, no life here.
Not with a bang, but with a whimper.
How will these bunker building individuals be viewed by survivors? Inevitably society rebuilds, yet these folks probably won't have anything of value to offer a new community. It's very possible they even lived a life of luxury while everyone else starved.
I think they will be in for a rude awakening when or if that time comes. To that end they're probably not building survival bunkers, they're building tombs.