In addition, Khepri declined to capture him while collecting parahumans during the battle against Zion, believing him to be "more trouble than he was worth".
His power seems to be related to some form of matter creation, which uses brains or perception as an attack-vector, since Wardens sought out All-or-Nothing brutes with resistant/non-typical brains and absolute matter annihilators to deal with him.
From the safe distance his power manifested as a 'storm', with colors taking on a rainbow sheen of impossible colors. The storm disrupts communications in the affected area, and can grow in size considerably. Other effects of this storm are unknown but it was enough to immobilize and contain the Simurgh.
The Mordovia Bubble was hit at the beginning of Scion's rampage, rousing Sleeper. He then traveled to Earth Zayin by portal and effectively cut it out from the greater humanity by settling near the portal and submerging nearby settlements in his power.
Using the Clairvoyant, Khepri found Sleeper sitting on a lawn chair on a balcony in Earth Zayin, reading a book out loud to himself. Deeming him too troublesome to collect, she let him be.
The Wardens attempted to utilize Sleeper against Simurgh and the Titans. It had little effect by itself, but following the intervention from Titan Fortuna the Sleeper's storm was able to capture the Endbringer. Following that the Sleeper had returned to passivity.
Wildbow has stated that Sleeper was included in Worm as a result of a fan's comment that not every character should be fully explained.
In the parahumans list, under Sleeper's power, Wildbow had a message with a caesar shift of 5, saying "As if I'd really put something here. For real."
Sleeper's name seems to be a reference to "let sleeping dogs lie" proverb, whose equivalent also uses the same sleep-metaphor in Russian language too, except with a specific evil bogeyman in place of dogs.
↑ 1.01.11.2The Simurgh lay prone within the storm that was the Sleeper. Unmoving. That hadn’t been him. That had been Dauntless, acting with the benefit of Titan Fortuna’s sight, guiding the direction of the blast.
The storm crackled, boiled, popped, the colors taking on a rainbow sheen that somehow felt it shouldn’t make sense with the way the colors unfolded. - Excerpt from Interlude 20.a II
↑ 2.02.12.2She’d heard about what it was, she’d seen pictures. When everyone at the Zayin settlements had still been getting set up, that same cloud had swept over them. Nobody had been able to get a message to them to warn them. They’d fled, but communication had been all over the place, a few people had been left behind, most of the others hadn’t fled far enough. The storm had swelled in size, and it had encapsulated every settlement in Zayin. It hadn’t been a large area, but it had still been mostly everyone, and it had included the portal the rest needed to get back. - Excerpt from Last 20.b
↑“I don’t suppose any of you feel brave enough to go up against Sleeper? Absolute invulnerability better than Alexandria’s, special brains, absolute annihilation powers?” - Excerpt from From Within 16.2
“Restless but still around. Earth Zayin in the palm of his hand. He started to emerge, Legend faced him down. [...] Leveled about thirty square kilometers of city.”
I nodded. “He’s dormant now?”
“For now. If he had motivations for making one attempt, he’s going to budge again soon. But I don’t have the instinct he’s our threat. He’s background. Someone else’s problem.”- Excerpt from Sundown 17.9
↑“First of all, the Sleeper is retreating. He is not an immediate danger, and we will let you know as soon as we can, if that changes.” - Excerpt from Last 20.b
↑"Wildbow: Sleeper was written in as a response to a fan saying that I shouldn’t go into detail and explain every character. He featured in a snippet I wrote back in the day (I spent ten years writing bits and pieces of superhero stuff before settling on the story I wanted to write) and seemed like a good one to drop in. He does have a power, but I think it’s best left unsaid, perhaps until the sequel." - Interview with Wildbow by t4nky