Dolphins Don't Continue Swimming After Being Attached And Reattached From A Lead.

Here is how to replicate it (This was done on a natural spawned dolphin):

Step 1: Put a lead on a Dolphin

Step 2: Reattach the lead.

The result is the dolphin stops swimming around normally and only moves for other reasons like to follow players and play with items and all they are, are a frozen mob unless you cause them to.

Picture shows what I mean, they completely freeze.