Superseding my previous answer, and due to the lack of detail and accuracy in the post quoted by this answer, I decided to rewrite it and hopefully clarify the exact functionings of this card.
What is a program?
A "program" is not much more than a descriptor for a hand revealed with The Grand Calcutron. As stated by the release notes (a.k.a. Unstable FAQAWASLFAQPAFTIDAWABIAJTBT):
Your program is still your hand, [...]
So what happens when The Grand Calcutron leaves the battlefield?
The release notes further mention something that isn't reflected on the card itself:
[If The Grand Calcutron leaves the battlefield,] the players pick their cards up and put them back in their hand. They are no longer public and no longer have to follow the rules of The Grand Calcutron.
A lot of technical details and interactions past this one are rather ambiguous, but in general, everything that interacts with a hand interacts with programs as well, in the same manner.
What if The Grand Calcutron is destroyed in response to it's last ability?
The ability itself is independent of the source and will resolve as normal.
When Grand Calcutron was still on the battlefield, those cards would be put in the program and revealed in the process, but now they're just drawn as normal and won't be visible to the other players.
Are there any even weirder interactions? How should they be handled?
There are a few weird interactions that happen if you look at the exact ways the rules work, and the way The Grand Calcutron is templated. For example, if you counter the first ability, players won't have programs and therefore would be prevented from casting anything.
In that kind of situation, assuming this wasn't deliberately done because it fit one player's strategy, you should probably go with common sense over rules and ignore everything but Grand Calcutron's fourth ability. As suggested by doppelgreener:
With the Un-iverse intention that "The point of Unstable is to lean towards the fun side of the spectrum", the idea probably would be: if your hands don't actually become programs, then you just use your hand as normal. The abilities on [The Grand Calcutron] apply to how we use our programs, not how we use our hands.
As with everything else in Un-sets, it's probably best to solve problems like this within your playgroup.