Spectrum_Legacy: Game shouldn't give up if ran on much weaker hw than min required, the user should however if experiencing discomfort or unsatisfactory experience. Minimum and recommended hw configurations are a thing for that reason too. The rest is about the art of neverending optimisations.
If the game is running so slowly that it takes too long for the player to be able to exit out of the game, then there's a problem.
dtgreene: I'm thinking of not so much targeting a framerate, but rather the engine taking desperate measures in an emergency situation, like if the frame time is measured in seconds per frame.
One potentially problematic situation is if, due to certain things happening in game, the game lags so badly that each frame takes minutes. At this point, the player is frantically pressing the escape key and hoping the game will respond, but then gets frustrated with waiting and then force closes the game, which is not a good experience for the player.
pds41: There are only really two issues which cause that - one would be the user running with insufficient hardware and the other would be that the programming, optimisation or design of the game is poor. If you've properly specified minimum and recommended systems and the users have appropriate hardware and set appropriate graphics settings, rendering so much that you're getting a frame a second or worse - or putting so much load on the CPU that you've got the same problem - is poor programming.
The best solution is to playtest to ensure that you don't end up with engine overloading situations for the hardware that it's designed to run on and to also optimise as much as possible to maximise the amount that can be on screen without issues occurring.
There's a third possible situation: The game, as the result of a glitch, some unintended behavior, or a mod, creates so many objects that even modern hardware struggles with it.
As an example, I'll look at a situation in The Elder Scrolls III: Morrowind that I have seen in a youtube video. There is one mod installed: Racer Recursion, which makes it so that, when a Cliff Racer is killed, two more immediately spawn. Now, the player can overload the game as follows:
* Create a spell that hits a large area, and is strong enough to kill Cliff Racers in one hit. (Cliff Racers have 45 health each, so on default difficulty a 45 point damage/drain health will do the trick.)
* Find a Cliff Racer in the wild. This shouldn't be too hard, particularly since there being too many of them is a common complaint.
* Kill the Cliff Racer, which will then cause 2 more to spawn, and repeat.
* Once there are a fair number of them, start using the spell, which will kill them and cause twice as many to spawn.
* Repeat until the game becomes a slide show, and repeat further and eventually the game will crash due to running out of memory. This can happen even on high end systems, due to the exponential growth involved.