The Idea Factory - The Plague of Dreams
Some event occurs, and suddenly everyone born from then on remembers their previous lives. Nothing before the event is remembered, but no new souls are born. Told from the view of one of the reincarnated, starting at their birth, when their mother is holding them, waiting for their soul to arrive. As the person grows up, they start to wonder what the event was and try to investigate it. It's not the first time they've done so, but they finally get a lead that goes somewhere. In the end, they must choose whether to reverse it, in the hopes of new souls being born from then on, or leave it, fearing that all would die off without it.