There's no internal state of the callee leaking out. The act of communication between the signaling site and the handling function is done via condition objects

There's no internal state of the callee leaking out. The act of communication between the signaling site and the handling function is done via condition objects - which are just like standard Lisp classes whose slots can be read by the handling function. The slots and/or accessor methods via which one can access the condition objects can (and should!) be documented as a part of the contract of any piece of code that is expected to signal conditions. Resuming execution is possible since the original stack is not destroyed by unwinding it. The handling code can simply perform a transfer of control to a point on that stack established earlier and continue from there.