i think it helps if it's an equivalent situation. like if my cat just died and you had a dog that died, that would be an appropriate thing to bring up in that moment. but i have a very tumultuous family life and i don't prefer it when people bring up their own family experiences in that case because the complexity and hurt is so different in magnitude, at least amongst my friends.

generally speaking when friends tell me something bad that happened in their lives i like to ask what they need from me. do they want advice, some kind words, for us to sit in silence while we do our own thing, food/snacks? i think giving people a chance to communicate their wants/needs after a shitty event in their life helps give them back some of the power they may have lost