Final answer:
The cornea is the avascular structure of the eye that can be donated without matching, as it does not provoke an immune response due to the absence of blood vessels.
Step-by-step explanation:
The structure of the eye that is avascular and can therefore be donated without matching is the cornea. The cornea is the transparent layer that covers the anterior tip of the eye and allows light to enter. Unlike the vascular tunic, which includes the iris and is highly vascular, the cornea does not have a blood supply, meaning that it typically does not provoke an immune response and thus does not require a matching donor. The sclera, while also being part of the outermost layer alongside the cornea, is not avascular and contains blood vessels.