Which decorative element is often seen over the quarter of a shoe or replaces a piece of the quarter when sewn in?

The correct answer is related to the function and placement of the decorative element within the structure of a shoe. Foxing is a strip of rubber or similar material that is often found on the upper part of a shoe, typically wrapping along the sides or over the quarter. It serves both a decorative purpose and a functional one, providing reinforcement and durability to the shoe.

When foxing is used, it can replace a piece of the quarter, enhancing the visual appeal while also contributing to the shoe's performance by protecting the seams and aiding in overall shoe structure. This dual purpose makes foxing a unique and valuable element in shoe design.

In contrast, backstay refers more specifically to a reinforcement stitch placed along the back of the shoe, the vamp is the front part of the shoe that covers the top of the foot, and the Goodyear welt is a specific construction method used to attach the upper part of a shoe to the sole. These elements serve different functions and do not fit the description of a decorative element that affects the quarter.