We hope all of you are doing well and staying healthy. This is a very new, very different kind of crisis. In the history of the United States, we can only think to the Great Depression where this amount of uncertainty to the future was held. That said, we are getting press releases that The CW is changing up their schedule to accomodate a potential pushed out date for many of their shows. Essentially, there are only so many episodes "in the can" right now. Once they've aired, that's it, no new content until it can be filmed. For instance, Supergirl, with only 20 episodes this season, has some of their finale filmed. They will need to edit together a new finale or wait until it's safe to film again.
This uncertainty is leading The CW to hold on to the episodes they have until more information about the current crisis is known. Speaking of crisis, however, The CW has announced that the week of April 5th, they will re-air Crisis on Infinite Earths. This will actually bring back Arrow to the CW for a week because technically one of the Crisis on Infinite Earths episodes is an Arrow episode. For now, please everyone stay safe and stay healthy. Rely on your local officials for particular information and for a wider set of information on the current situation, visit only trusted sources like the World Health Organization.