While flying, I took a cow on a lead, and drag it into the air.
Then, I right clicked the cow to detach the lead. The lead disappeared, but the cow was still flying, and I was still able to move it by flying to the right or left, like it was still on the lead.
When I right clicked the cow again, I saw the lead appear for a second and then it finally disconnected the cow.

Sometimes, the bug does not appear. It'll most likely happen when you right-click the mob when it's just out-of-reach for the server, but not the client.

I also noticed the opposite can happen: the mob will be on the lead, but still be able to move (and/or fall down).

P.S.: the cow died.