Curate, connect, and discover
Ulquiorra’s jjk verse could be that he's a special grade curse born from the feelings of emptiness and void. souls of people who have been consumed by the void are the primary source of his energy. I'm assuming all the espada are special grade curses just like how they are the highest rank in their own verse. Anyways, will also be assuming that in this verse Aizen is still a drop out and recruits him along the other curses. this is not the main verse but a war that took place decades or hundreds of years before the main events, so somewhere between heian and modern day. His state in present jjk-verse is a dormant curse that has been affixed to a sword, just like his other 9 "comrades" and are kept in the hidden inventory at hq.