Sorry, I laughed. I'm astounded by how much the British like puns as opposed to Americans. I've heard British audiences audibly gasp at the high quality of a pun, like it took their breaths away.
Reductively I'd say the prey is the audience in that case, for not being smart enough to see it coming. The best puns are heavily telegraphed yet somehow totally unpredictable. They're clever mirrorings of things everyone is already familiar with, but still didn't see coming.
Bad puns aside, there’s many theories in the scientific literature (from cognitive psychology, linguistics and AI) that describe the mechanisms of puns (and many other types of jokes, really), and they mostly talk about deviations from a script/subverting expectations and norms (Hanks’ theory of norms)/accessing a non-default interpretation that is different from the default one (Giora’s optimal innovation hypothesis).
I don't think that unexpected things are necessarily funny. Unexpected stupidity or weakness is funny. Unexpected cancer isn't funny. To make it funny, you have to make someone stupid.
As you could imagine, the theories have that as a core idea, but are more detailed than that. Nobody ever thought that unexpected = fun.
Among other things, there’s different level of unexpected, something that bends the laws of physics (the cartoon character suspended in the air for a while before falling down) is more funny than, say, the character speaking japanese.
To criticise a theory it might help to read it first…