It has been suggested that the airlines must keep flying their normal routes, or they will lose those routes. I know nothing of the industry so I don't know if that is the case.
I heard the same thing about the slots. To ensure that some aircraft do not fly around empty for this reason, the Lufthansa Group had already submitted an application to the EU a few weeks ago. The request was that all airlines keep their slots even if they do not fly. I do not know the result of this request and I do not know how high the proportion of aircraft movements is for the reason of not losing their slots.