Playing Romancing SaGa: Minstrel Song (PS2), and remembering one incident that happened:
I was fighting the Ghost Ship boss with an underpowered party. (I would say underleveled, except that this game doesn't have conventional levels and XP.) The thing is that this particular boss, unlike most JRPG bosses, is not immune to status ailments. So, my strategy was to paralyze the boss, which I have had work before. However, things did not go according to plan. I think what happened was something like this:
Round 1: Enemy manages to wipe out most of my party, leaving only Claudia alive. (I don't remember whether I got the spell that can inflict paralysis off, but if I did, it did not work.)
Round 2: (Most of my party is down, so things are not looking good at this point.)
* Claudia's turn comes up, and she's about to attack with her bow.
* A lightbulb appears over her head. (This is normal, and is how you learn new physical techniques.)
* Claudia uses Shadow Shot (bow technique that does damage with a chance of instant death.)
* The instant death effect *works*, killing the boss (that I was sure I would not defeat this attempt) instantly.
Of course, I have other memories, like when I was playing Final Fantasy 6 (PSX version, though it doesn't actually matter for this purpose) and got softlocked; I had Gau and Umaro, both uncontrolled and using only physical attacks (and some healing from Gau), but able to absorb elemental attacks; the enemy had turned invisible (making physical attacks always miss) and was healing my characters with elemental attacks; and the game would not let me run away from this particular enemy, hence the softlock. (This is worse than a game over; in FF6 (but not other FF games), you can continue after game over keeping the XP (but not other things) you gained since your last sav, but in a softlock situation like this, your only option is to reset.)
Also, in Destiny of an Emporer (NES), I was unable to complete the game because a glitch caused a key item to disappear from the chest it was supposed to be in.