On a summer evening six years ago, the Italian tennis player Stefano Travaglia walked from his family’s sixth-floor apartment in the town of Ascoli Piceno near the Adriatic coast to the floor below. He needed to pick up some tennis shirts onto which an elderly neighbor had sewn sponsor patches for him. He bypassed the building’s elevator for the short trip, taking the stairs.

The simple errand turned disastrous: Travaglia’s flip-flops slipped on the recently cleaned floor, and he crashed down the stairs. He reached out his arms to protect his face as he crashed toward a plate-glass window at the base of the flight of stairs, and his right arm went through the glass. He also sustained cuts to his left arm, face and shoulders, but his right arm sustained the most damage.

Travaglia’s parents, both tennis coaches, heard the collision and broken glass, and came out of the apartment to find their son bleeding profusely. As his mother drove them to the hospital, his father held his son’s wrist trying to stop the bleeding, Travaglia said. One hand had not been enough to stop the flow from a severed artery, so he clutched it as best he could with two.

Travaglia made it to the hospital semiconscious, but knowing he would have died if his parents had not been there to find him. His mind next turned to his right hand, which he could not move.