No, it is not possible to fall to your death on the moon in the traditional sense. The moon's gravity is much weaker than Earth's, approximately one-sixth of Earth's gravity. As a result, objects and individuals on the moon weigh significantly less and experience a lower force of gravity.
If you were to jump or fall on the moon, you would experience a slower descent and a more extended period of time before reaching the surface compared to Earth. You would also have the ability to jump much higher and cover greater distances due to the reduced gravity. However, because the moon's gravity is still present, you would eventually land on the surface.
In summary, while falling on the moon would feel different and have different consequences compared to falling on Earth, you would not fall indefinitely or experience a deadly fall as long as you remained within the moon's gravitational field.