@sepiapages The same thing happens on my end as well. The lead item drops, but texturally it's still wrapped around the fence post. However, I didn't include that in the bug description because I believe that issue is covered by MC-96347. However, that is also an annoying factor.
@CometAurora Interesting. I had thought it was the pathfinding causing them to break the leads, but from your experience it looks like it might just be that they move too fast and erratically to be kept tethered with a leash.
Since you are using the Fabric mod, it's very possible that it is causing your issue, and therefore not a reproducible bug.
I'm no longer able to reproduce this bug in 1.21.1. Is anyone else still able to reproduce this behavior, or was it sneakily patched somewhere between 1.20.4 and 1.21.1?