A Nihilist is more stable than you think. A tree doesn’t need purpose to grow, and neither does a human. Instead they follow a process that’s expressed by the body in response to the environment. For humans we not only have physical sensation but also memories, ideas, and thoughts. Without a worldview these all still happen, and your body will still react to your thoughts and sensations without a purpose. A healthy Nihilist would not feel sad about having no meaning, since they never had one anyway; on reflection, they might feel happy that there’s no obligation to respond other than how their situation moves them to. A Nihilist can do what is morally right without the restrictions of a purpose that proscribes them to do otherwise.