I've never seen a Pokemon actually die in the games, and it shouldn't be able to happen, but your story sparked a memory of my time playing Red, so I thought I would respond.
When I first played Red, I only trained my Blastoise, and barely caught other Pokemon. I didn't exploit glitches or anything else, so every level my Blastoise gained was due to my own dedication. When my Blastoise's level started to get fairly high (80ish, exceeding that of my friends' starters, who they'd had for several more months than I had had my Blastoise), some classmates informed me that my beloved starter would die upon reaching level 100. I had no validation of the outcome either way (I didn't spend much time searching the internet on my dial up connection back then, and there wasn't that much Pokemon info out there), so as my Blastoise approached level 100, I began to dread its imminent passing. I tried to gather as much information as I could, but without much to go on, I eventually took the plunge and leveled it up (I planned on turning off the game without saving if anything went wrong, but of course, I leveled it up vs. the Elite Four, so the game saved anyway).
Incidentally, my Blastoise was fine, although further experience points did nothing for it. Since then, I've leveled up plenty of Pokemon to 100 across the generations, with no ill effect. (Although I'll admit that I tend to prolong the 99--> 100 level up, as things just seem so final, and in some ways, "dead," once my Pokemon can't accept any more experience points.)
So, in answer to your question, no, I've never heard of the player's Pokemon dying in the games except from ill-meaning neighbors and classmates, childhood nightmares, hacks, and creepypastas. I could see Pokemon disappearing due to glitches or the like (or even a friend or sibling releasing them, trading them, or storing them on Stadium, unbeknownst to you), but I've never heard of Pokemon dying, and I'll admit that I'm skeptical of your claim (though I don't deny that that may be what you remember having happened). At this point, I think the R/B code has been analyzed fairly thoroughly, so I can't see any way for Pokemon death having been included without anyone realizing it.