What happened to Claire?

It seems that the director and writers meant for it to be a mystery or left to to the viewers' imaginations. There's nothing in the film itself that conclusively shows what happened to Claire.

Karyn Kusama and Phil Hay (the director and one of the writers of the film, respectively) on their Reddit /r/movies AMA (Ask Me Anything) post, say that they won't comment about it, when asked about what happened to Claire.

thedeliman1: ...Is Claire alive?
KarynandPhil: ...Can't comment about Claire!

Most likely Claire lives. The movie builds suspense around her leaving, but ultimately I think that was just to add to the atmosphere and was actually just a red herring.

If Pruitt did kill Claire, it would have had to be fast. He was not gone long so we have a rough time frame for him to do it. Possible, but tight. It would have also needed to be quiet as you could hear them talking faintly from outside the window, so no quick kills like a gun. The next thing is that when Pruitt returned he wasn't covered in blood and wasn't missing his jacket, so stabbing and other more gruesome methods that are fast are also narrowed. Pruitt also needed to move Claire's car afterward since, as we learned late in the dinner it would have been possible for someone to walk in on Pruitt trying to kill her. It's possible that with movie magic she could have been killed, disposed of, and explained away, but I really don't think that would be in line with Claire's character or the motives of Eden, David, and Pruitt.

Claire lives because she is the vanilla character who, when confronted with a choice to stay in a risky situation says, "Nah, I'm good; later guys." In the film, we see both Claire and Will having thoughts that the party is weird. Claire makes the reasonable decision to leave after Pruitt shares his backstory and the game they were playing got kinky. Knowing what we know about another key plot point in the film should also alleviate some concerns over her fate.

One last spoiler mention is that:

All of the violence was impromptu, it wasn't a murder party, it was a mercy killing. In fact, had Gina not drank a quick sip of wine and died (alerting the rest of the group that things were deadly), it is likely they could have turned the group against Will. He had just knocked down Sadie and they could have toasted that she was okay or they could have just insisted that Will was in a mad spiral. He had no proof, and it was only when Gina died of poisoning that suddenly David snapped and started killing. Pruitt followed through since it had been started and couldn't be undone. No one was in danger until that final toast of the night. Choi and Claire were just to deceive the audience on WHEN things would hit the fan (since it is a thriller we all knew it would so that was never in question).

I do not belive Claire got killed. The plot reason for Pruitt catching up with her, is ofcourse to make us think he kills her - but if we start thinking about the rationality and motivations from the killers, it doesn't make much sense to kill her in that moment. Their reasoning for murdering everyone is some twisted sense of mercy. (This ties in to Will killing the animal hit by the car in the beginning). It's not that they WANT to kill everyone. They see it as their "duty" to deliver the mercyfull death to all those who suffer. They probably see Claire leaving as more of a "that's her loss", and try to make her stay, but they wouldn't want to jeopardise the whole plan just to get her. Also - the timeframe that Pruitt is gone doesn't allow for a well executed murder. He would have had to leave both the body and the car in the street. And risking a visit from the police during a crusial point in the evening wouldn't be in their best intrest. I think he simply tried to convince her one last time, but seeing that it was no way to change her mind, just let her leave and went back inside.

I think that Claire got killed. Note that Pruitt comes back with a jacket. That's kind of odd as he has no actual reason to wear it inside. The only reason for him to carry it back is to hide his arm or fist that's probably covered with blood. Also, he looks like the strongest of the group and has history of assaulting women. Moreover Will is not only quickly distracted by David (this coordination cannot be of coincidence) but also challenged with direct statement that he watches his friend going to a car.

Good ending I thought...as far as Claire goes, maybe she got lucky and on her way out picked up the 2 that were lost or maybe got out from their own cult invitations, told claire about it, claire put the stories together, FINALLY got some cell reception and called the cops. Personally if it were me I would have left the party after they played that eerie cult video hahaa or after slapping that bitch back..what was that?

Yes, in the commentary she revealed Claire was shown dying in the bushes right before Will goes into his son's room but it was later deleted.

Director Karyn Kusuma told in a commentary that indeed Claire was killed and the scene of her dying in the bushes was trimmed out.

Sources:

https://filmschoolrejects.com/commentary-the-invitation-70bec3d75e61/ http://bloody-disgusting.com/editorials/3399511/5-things-didnt-know-invitation-including-shocking-revelation/

I think we were to assume Pruitt killed her after stopping her And the two looking for a party were trying to escape another cult

Actually, claire was killed. It was in a deleted scene, she was attacked by pruitt in the bushes.

The director revealed this in the film's commentary.