Killing a leashed mob does not drop lead

I broke my sword on a cow on the first hit so I had to chase it around and beat it to death with my hand. I saw the lead in my hotbar and had the great idea of leashing it so I could stay in one spot and just turn instead of running around. It worked to perfection, but once the cow died the lead just disappeared.

I expected it to be just like when you right-click a leashed mob to unleash them, and that the lead would drop where it had been standing. However, no dropped lead, just the usual leather and beef.

Steps to Reproduce:
1. Put a mob on a lead
2. Kill mob