The last thing a person needs to hear is that there's something wrong with how they work through their pain. A better approach is to simply say that you went through a situation like theirs, without going into detail. That gives them the option to talk about their feelings if they want to, and acting as a shoulder on which they can cry, vent, or plan vengeance is the most valuable thing you can do in a time of mourning.
A related bad-news-bears expression when you get bad news about what those bears did is advice to "be strong." This is often heard in the context of not crying in front of a child and making him or her feel worse. It's a tough-love way of reminding you that there are still a lot of wonderful people in your life, some of whom may depend on you for guidance. But the implication is that you're being an overemotional wimp.
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"Hey, don't cry. You barely got to know that puppy."
Grieving is already one of the most emotionally complicated processes that a human being can go through -- telling someone to repress part of it by finding their inner RoboCop isn't going to help. Go ahead and let it all out, as long as you don't grieve by punching people in the face, or shooting up sympathy heroin.