question about television networks...?

i really don't know much about television networks. but i have a question.

let's say someone had a live tv show on a network. "the Mary Hart show" for instance.. and the ratings were very high. let's just say this "mary hart" decided to step away from the show for good because she has no interest in continuing. is there anyone in particular in charge, that would most likely attempt to convince her not to leave in order to keep the ratings up? if so who is more likely to do it? sorry if this is a horrible question.. like i said i really don't know much about this kind of thing and it's sort of personal why i'm asking.