It's really hard to tell the truth when you think someone will discount or invalidate what you say. Whoever is listening may not even mock you or try to make you feel bad. Still, just by acting astonished or as if what you said is incredulous, she gives you the message that you are batty. Then, you want to clam up. Worse yet, if he tries to solve the problem or ask a lot of questions, like "why?," you're left befuddled and depressed.
So, if you want your dear family member or friend to come clean, be sure not to overreact, or even react very strongly, if the persons makes an honest confession of something embarrassing or some weakness or failure. The best thing to do is thank him for being honest, express understanding of how difficult it must be to deal with the situation and ask how you can help. If you have an educated guess as to what's going on emotionally, you could also venture to state it empathetically, like "maybe you feel like that's your only way of coping with scary stuff." If you're wrong, he'll correct you, knowing you tried to understand in a nice way. If you're right, she may open up and discuss it more. Either way, you won't shut down communication.
Watch you reactions to your loved ones and see what happens.