When a liquid droplet is deposited on a flexible sheet, the sheet may deform and spontaneously wrap the droplet. We propose to address a problem in connection with this "capillary origami" experiment: does a flexible rod put in contact with a liquid droplet spontaneously winds itself around the droplet? In the positive situation, what is the maximum length that can be packed inside the droplet? We will finally try to connect this problem to damping issues in spider webs.