A piece of the moon could become a near-Earth asteroid through a process called gravitational slingshot or the lunar escape velocity. Here's how it could happen:

1. Impact Event: A large asteroid or comet collides with the moon, causing a chunk of its material to be ejected.

2. Ejected Material: The ejected material, a fragment of the moon, is launched into space with a significant initial velocity.

3. Gravitational Perturbation: As the ejected material travels away from the moon, it experiences the gravitational influence of the Earth and other celestial bodies in the vicinity.

4. Perturbed Trajectory: The gravitational interactions alter the trajectory of the ejected material, causing it to deviate from its original path.

5. Earth's Gravitational Influence: The Earth's gravitational pull becomes more significant as the material approaches the Earth's vicinity. If the conditions are right, the ejected material may be captured into an Earth-centered orbit.

6. Near-Earth Asteroid: The captured material, originating from the moon, would then become a near-Earth asteroid, orbiting the sun in a trajectory influenced primarily by the Earth's gravitational field.

It's important to note that such events are extremely rare and require precise conditions for the ejected material to avoid being pulled back to the moon or escaping entirely from the Earth's gravitational influence. However, the possibility remains, and such moon-derived near-Earth asteroids may have played a role in delivering water and other volatile materials to the Earth in the early stages of its formation and evolution.