Sheriff Hassan died.
The first gunshot wound he received was in the left thigh, but the second was in the stomach, about six inches above his belt.
Midnight Mass - S01E07 - "Book VII: Revelation"
Blood is visibly flowing from the stomach wound as he and his son hobble toward the beach, and he drops to his knees at one point, clearly in bad shape. He's also never shown walking without his son propping him up.
Midnight Mass - S01E07 - "Book VII: Revelation"
The actor playing Hassan, Rahul Kohli, discussed the character's final scene in an interview with Alex Zane, and it's very apparent from their discourse that Hassan died. I've transcribed two relevant portions of the interview below -- from around the 1:52:23 and 1:56:11 marks -- but there are other references to Hassan's death in the interview as well.
ALEX ZANE: So, I mean it's beautiful, because obviously, like you said earlier, you and Ali are reunited. You're together there, you're praying together. You've been shot, by Bev. It's a stomach wound. You're clearly gonna die.
RAHUL KOHLI: Yep.
ALEX ZANE: And, just that bit where you sort of slump over, to the side. And it happens in exactly the right order. Because after everything they've been through, you know, the big fear would be that, you know, Ali would burn before Hassan died. And it's so important that Hassan does die.
RAHUL KOHLI: You're right. I never thought about that. I never thought about that. You're right, yeah. He doesn't need to watch that.
[...]
RAHUL KOHLI: As an actor, I've got to make sense of it. I don't want anything to look stupid, right. Especially death. Like, watch Dark Knight Rises, for instance. There are some final deaths that look weird. It's always in the back of your mind. You want to make sure it has the right meaning and moment. So we shot in two locations. We shot on the beach. On real a beach in Vancouver. Rahul [Abburi] and I. Quite early. I think I did this quite early into our filming. So we do it with real, the real sunrise was done, so we did it for real. And, you know, we're doing our prayer. And then at some point, you know, Mike's [Mike Flanagan's] like: "And Hassan dies." And I tried to find the most dignified way of collapsing, knowing it wasn't going to get used.
Rahul Kohli II (Midnight Mass Spoiler Special) - Full Interview
For reference, Mike Flanagan -- mentioned in the quote above -- was the director and one of the executive producers of the series.
