When something's sagging or hanging limply, it's drooping. It hasn't rained in over a week: it's probably time to water those drooping flowers!
After a long, hot day, the fancy hairdo you carefully gave yourself this morning may be a drooping mess. And even the perkiest runners can usually be described as drooping by the end of an ultra-long marathon. Anything that droops, or sags in exhaustion, weakness, or melancholy, is drooping. The words stem from the Old Norse drupa, "to sink or hang the head."