I ask because I have recently seen monsters roll a 20 against a DC which when added to their ability bonus (Fort, Reflex, etc) still means they should fail the DC, yet they save against the effect. This is hard, but you can live with this.
What worries me more is that if a pc has no device given immunity against an effect and rolls a 1, even if their basic save is higher than the DC needed, then does that mean they fail and take the full effect. This is worse than the scenario described in paragraph above.
To add to what has been said above, the chance of a critical success (rolling a natural 20 in a d20-based system like D&D) is a pretty deeply ingrained concept. It adds another layer of randomness to the already randomized nature of the game. What rolling a natural 20 usually represents, in a more IC sense, is that in that moment, everything went perfectly right for you. There are optional rules that add even another layer to the critical success, bringing another die roll into play that determined additional effects (extra damage, loss of limb, etc.). It also represents the idea that there are no sure things, by including that possibility that despite a significant difference in power, the underdog can get lucky. This applies equally to monsters and PCs alike, which is only fair.
Of course, this concept applies to other things besides saving throws, notably to-hit rolls and skill checks.
Many GMs subscribe to the concept of a critical failure too, which would be rolling a 1 on a save, to-hit roll or skill check. Mechanically, our engine does not support a critical failure for saves, though our GMs (including Leanthar) usually do. Discussions about critical failures usually draws some heated responses and ardent supporters. No one like to fail really, but sometimes failing is fun...at least OOCly.
The only thing I'll say about a chance of failure is that it is something that people should be prepared to accept, even if by all rights they
should succeed. Everyone has bad moments. Especially in RP-heavy situations, even the most powerful, accomplished PC should expect that there is a chance to not succeed. If this were not true, either everything such a PC attempted would succeed automatically, which is ultimately pretty boring, especially for everyone else nearby.
With that, and the above all said, mechanically speaking, there is no critical failure for rolling a 1 for a saving throw, either for PCs or NPCs. In RP situations, players should be prepared for a GM to treat a natural 1 to be a failure. This will vary from GM to GM, as will the consequences of such a failure. Roll with it though (no pun intended). Sometimes, great things come to those who fail.
