How they encourage her to hold on to her belief?

Which character are you referring to by "her"? What belief are you referring to?

so if you are talking about kate and her belief that larry is still alive then the answer is

chris and joe keller never confront her they let kate believe that larry is alive and that he is coming home chris wants to put an end to her belief so he tells his mum that waiting for larry is like waiting at a railway track for a train that is not coming and that she should accept the fact that he is dead because nobody comes back after three years his main reasing for saying all this now is because he has a motive if he wants to marry ann he has to convince his mum that larry is gone for good