You should double check that you are understanding correctly what they told you. My agency has pretty strict ethics rules yet it would be pretty unusual to have to recuse from nearly all duties, unless you are at a financial regulatory agency and trying to get in with the main companies you regulate, perhaps. Even then, they ought to be able to find you other duties. It's not like no one has ever left before, so figure out who did so recently and contact them to ask how they did it.