It is not up to us to decide if the threat is real or theatrics. We may have experience with the A, but not the training to deal with it. A professional should be involved by calling EMS if you know where the person making the threats is likely to be found.
I've had to make this call to police on an alcoholic friend. The EMS felt that what he was saying should be taken seriously as a threat of suicide and they acted upon it. They went and got him and brought him to a hospital for evaluation. He was spitting mad at me for having to spend the afternoon at the hospital being assessed and for wrecking his day as "obviously" he would never have done anything. No concern for the worry and heart-wrenching fear he had put into the hearts of his family and friends. I told him I had no choice on whether to make the call. He, however, had the choice to make the threats or not.
My heart goes out to those who feel compelled to actually carry it out, and all their families.