I have managed several of these posts in the past and they can range from serious problems and actual suicide attempts to trolling. Every case is individual.
What we did was:
1) Identify who on the mod staff would contact the person. It is important, IMO, to have a single contact and we had the advantage of having people with some background in suicide prevention. If you do not have official training, most any staff member can help.
2) Close and delete the question. With the exception of trolls, I have NEVER seen a complaint about deleting the post/question. This is to protect both privacy and unwanted attention to the OP.
3) Maintain frequent and supportive contact. Offer compassion and alternate options. Ideally, guide the OP to professional assistance, suicide hotline typically. You can find them via google search.
If the OP is unable or unwilling to help, you as a staff member can make the call. At a minimum you will get some advice form people actually trained to manage such a crisis.
4) I will caution you that there are times when such treats result in an actual suicide attempt. Depending on your training and background, staff may need help as well, either from each other or professional.