Why does a lens still form a full image when the front element is partly blocked or damaged?

A lens can still form a full image because each small area of the front element receives light from the entire field of view, not just one small part of the scene. The lens then bends that light so it reaches all parts of the sensor.

So if you block part of the front element, you usually do not lose part of the image. Instead, you reduce the amount of light entering the lens, which mainly makes the image dimmer. The same basic idea is why many reflecting telescopes still show a complete image even though the secondary mirror blocks part of the incoming light.

Similarly, damage to the front element often has less effect than people expect because the rest of the lens is still contributing light from the full scene. Front-element damage may lower contrast, increase flare, or reduce transmitted light, but it does not necessarily prevent the lens from focusing a sharp, complete image. In short: partial blockage or front-element damage usually affects light throughput and image quality more than image coverage.