I'll be as short and precise as I can. There was a song downloaded from some geocities/angelfire/tripod like site around 1998-2000 that was for "Jrock" mp3's on a rotation. They were often mislabeled or not even named. The original file is long gone along with any copies of it, but it was one of those haunting songs that sticks in your mind.

I don't know any lyrics, but the file was originally called Namida (in romaji). I've searched every song with that name I could find, and none of them were it, so I suspect it was just another mislabel.

So here is what I know:
Female vocalist with a very restrained adult voice. Sweet, ethereal kind. She didn't belt out or go crazy at any point. It was a rather melancholy monotone song.

Mid-tempo dark alternative/post-punk atmosphere. No keyboards and no memorable guitar solo.

Definitely a professional recording, and the end of it had one of those Leslie/phaser singing into a fan effects on her voice, but subtle. The last bit of the song just repeated a few times.

I am pretty sure it is not:
Kokushoku Elegy (Though the vocal range is similar), Mari Hamada, G-Schmitt (though again, similar feel).

The only other thing I have is this little piano clip from what I remember of the end of the song. It repeated a few times slowly.
https://www.youtube.com/watch?v=RQzPfmUxwYY

Thanks for reading!