Freak out and fawn, begging them to stay

wish publically that they would stay, ask if there was anything you could do to help

wish publically that they would stay, but also make note that if they feel they want to go, you accept it

publically mention their reason for leaving isn't valid and they are looking for drama

privately roll your eyes and move on to the next artist. You'll miss person X's stuff, but s/he's not the only one on here

Other