Scholars have been pondering this for centuries... or at least Touhou fans who are unfamiliar with PC-98 and can't name that last character in Bad Apple (before Reimu and Marisa show up again at the end) have... and it's probably only been like a decade or so but anyway I digress.
Elly appears in the 4th game in the Touhou Project Franchise, Lotus Land Story. Elly is the third stage boss. She guards the gate of Mugenkan, a mansion situated between the real world and the dream world, owned by Yuuka. Unfortunately, Elly doesn't get that many encounters during her workday and claims her battling skills have gone rusty as a result, saying "I couldn't help it! I couldn't help it! It's been a while since I've fought!". When Reimu (or Marisa) encounters her, Elly sheepishly admits she had been defeated already today by Marisa (or Reimu), but seems determined to keep anyone else out of Mugenkan. Elly has some tricks up her sleeve, she has the ability to throw her scythe like a boomerang and can throw floor tiles at the protagonist. Reimu (or Marisa), defeat her anyway...
Aaaand that's it! That is Elly's only canonical appearence. She never appears again after this. Wherever Elly is now in canon, I hope she is doing well.
I'm sure you're wondering, "Ok... so why do you like Elly? Why is there a fan site about this charater who shows up once and never again. Why do fans like her anyway???" Well there's a couple of things. First of all, she's fabulous. Her hair is ON POINT, ok? Second, she has unique abilities no other Touhou character has. Third, Elly is the face of Bad Apple. Even though, funnily enough, it is only her stage theme (although her main theme "Spirit Battle ~ Perdition Crisis" is also a banger and highkey underrated). Bad Apple brought Elly into the spotlight, and rightfully so. Bad Apple's melancholy lyrics add a lot of nuance to Elly's character, something missing from her original depiction. Even if Elly may not be as popular as Flandre, Cirno, or Sakuya, Elly has received plenty of amazing fan art, music covers of her themes, and fan comics and fan fiction.
Also she makes this face and it lives in my head rent-free.