Remnants of Despair

After their leader died in The Ultimate Punishment, most members of Ultimate Despair followed her example and committed suicide. The ones who survived became known as the Remnants of Despair 

Eventually, the Future Foundation secured the custody of fifteen of them - at first only aware that they were survivors from Hope's Peak Academy. When Makoto Naegi, by that time a member of the 14th Division of the Future Foundation, realized that the survivors were in fact, the Remnants of Despair, he quickly directed them to Jabberwock Island in secret. Makoto made them enter the Neo World Program, where their memories were reset to a time prior to their entering Hope's Peak Academy, before they were manipulated by Junko - resulting in them not recognizing each other. The plan was to overwrite their memories with good ones, to undo all the damage Junko had done to them.

Unfortunately, this plan ended in failure, due to Junko's interference as a virus AI, uploaded into the program by Izuru Kamukura right before they were put into the program. As a result, they ended up experiencing much of the same violent events as the "Class of 78" did, albeit in a realistically-simulated environment. By the end of the incident, ten of the original fifteen became comatose. 

The ending of the Danganronpa 2: Goodbye Despair heavily implied that even though the Neo World Program did not erase any memories, the remnants of Ultimate Despair who had made it out of the Neo World Program have kept their memories from inside the Neo World Program, and were assumed to have recanted their beliefs in the concept of despair itself, thus leading them to abandon their status as Ultimate Despair. The surviving Remnants of Despair currently reside on Jabberwock Island and are attempting to find a way to awaken their comatose friends, while the Future Foundation left them alone and continued cleaning up the world and putting an end to The Tragedy.

After the events of Danganronpa 2: Goodbye Despair the Remnants of Despair still active in the world are few and in disarray for both their decrease in number and lost of prominent members like Junko and Izuru.

However, they still continued with their terrorist activity managing to carry out forty attacks in only a month. Despite that, they are described as on the verge of extinction by Monokuma

More Information 

Ultimate Despair are described as a group of people who have "become despair". As Junko describes despair as a sort of contagion/state of mind, it can be inferred that the members of Ultimate Despair are those who have been "infected" by despair. Their goal is to spread despair across the entire world, driving it into a state of self-destructive anarchy.

They started The Tragedy and kept it ongoing even after their leader's death. 

They defied understanding and did various things for the sake of despair and Junko Enoshima: some starved themselves till their bodies were husks, some offered up their parents to Junko to use for experiments on murder, others slaughtered innocent civilians and forced them to kill themselves as a tribute to their dead leader, one removed their own eye and replaced it with Junko's, possibly to see her despair. 

It is also said some members of Ultimate Despair attempted to produce children with Junko's corpse. It is notable that although many other members might have done similar things, Nagito Komaeda is the only person whose act was fully established; he took Junko's left hand and sewed it onto himself, resulting in him having a non-functioning left hand.  

Another interesting fact is the majority of the people who became Ultimate Despair have their eyes turn red or crimson. It was never explained why this has happened, but the most likely reason is that it was a result of the psychological change in the members when they fell into Despair.