Pretty much anything about him beyond his name is a HUGE spoiler for season 2, so you've been warned...
Like his fellow members of the Eliatrope Council, Qilby reincarnates after death. But while he (as well as, from what I understand, his twin sister, Shinonome) remembers all his past lives, his siblings' memories are almost completely wiped when they die, with only hints of emotional or subconscious memory lingering in their new incarnations.
This means Qilby and Shinonome are effectively the oldest of their siblings... and it also means they're condemned to die repeatedly and remember every gruesome second, and to watch their family die and forget they ever existed, over and over and over, for the foreseeable eternity.
It also means eventually, every part of life that once seemed interesting or exciting has become hopelessly stale and repetitive.
By the time Qilby first appears onscreen, he and his twin have been enduring this for at least several millennia, and it's taken a catastrophic toll on Qilby's mind.
But what was life like before that?
Before his damaged mental state is revealed to the audience, it's shown that Qilby is very good with babies.
This, combined with his "oldest child" status and the absence of their parents, has made me fall in love with the headcanon that in his younger and more mentally stable days, he and Shinonome were the ones who raised their more forgetful siblings whenever they died and were reborn.
I like to think they had a series of actions they repeated whenever their siblings came back to life - songs, childhood stories, favorite games - in an attempt to awaken the embers of emotional memory and reestablish their bonds.
The lyrics in the image are for one of those songs. I kept picturing Qilby and Shino singing the Turret Opera from Portal 2 to their baby siblings, and I decided to adapt the lyrics into something more fitting for the lonely existence of those doomed to be forgotten.
You can listen to the Turret Opera here, if you don't care about end-of-game spoilers for Portal 2.
If you want the lyrics in written form, here they are:
Hello, child, glad to see you again
Though I know you forgot
All our memories
The bond we once had
I will remind you, once again
Love forgotten, but I
Know I can earn it once more, and then
You’ll forget, I’ll earn it again
We’ll make lots of new memories,
Replace the ones you have lost
As it’s always been
It will always be
I can’t do this anymore…