Michael wasn't exactly the strongest vampire he knew; he was actually the youngest in Morganville and the weakest, vulnerable to things like sunlight and silver in a much more intense way than the older vamps. Someone like Amelie or Oliver could survive a stake to the heart if it was pulled out fast enough or a walk in the daylight if it didn't last too long, but Michael would start smoking the second he had any exposure to the sun and silver was a hell of a lot more poisonous to him at his age than the others. It made going out into the unknown of this maze somewhere between stupid and suicidal probably, but he couldn't face the alternative? Sit safely inside the apartment while people were in danger? Hope and Lizzie were new friends, but they were still friends. There was no way he was letting Hope go in there without him, whether the Entity kept them together or not.
He at least had the sense to pick up one of the backpacks, which super conveniently had some things that could come in handy if it started to get sunny in there. If that happened, he could cover himself with the blanket, at least. It was at least some hope that he wasn't going to die in there. Again.
The inside of the maze was fucking creepy, but Michael did his best to focus on why he was here and ignore the sounds and screams around him. Finding Hope quickly helped and so did the fact that he could see easily in the dark. Vampire senses came in handy.
While Hope challenged the guy with the axe, Michael moved from where he'd been standing just behind her to slip around axe-guy and try to get to Lizzie, who he was sure was on the other side, despite what his eyes told him after Hope's incantation. He'd meant it when he said he trusted Hope could handle herself and he wanted Lizzie to know she was safe now, even if they definitely needed to get rid of this guy and find a way back out before that would be technically true.