What is the ruling on threatening someone by exposing a sin they committed, and what should I do if they are going to expose it?

There is no harm in paying money to someone who blackmails you; however, one must be cautious that the blackmail does not escalate, and that forbidden things may be demanded. Suicide is greatly forbidden, and its recompense is Hell. One must rely on Allah and rid oneself of the idea of suicide, and ask Allah for protection and well-being. If there is a benefit in paying money to ward off the evil of the blackmailer, then there is no harm in that.