die a natural death
1. Lit. [for someone] to die by disease or old age rather than by violence or foul play. I hope to live to 100 and die a natural death. The police say she didn't die a natural death, and they are investigating.
2. Fig. [for something] to fade away or die down. I expect that all this excitement about the scandal will die a natural death. Most fads die a natural death.