groak n. - to
stare at someone who is
eating in the
hope that they will
give you some of their
food.
This is something my dog does very frequently. When I'm eating, she quietly sits in front of me looking at me, and slowly she starts to look neglected and uncared-for until I finish, at which point she rushes gleefully to her bowl to see if I am going to give her any scraps.
The Chinese have an expression: "He that lives on hope will surely starve."