Something bad happened. Some people are sad. Let's bring up the topic of suicide and make sure they are all aware of it!!!!!!!!!!!!!!!!!111111111111 And then feel good about how kind and helpful we are.

People already know suicide hotlines exist. If they want one they can google it or siri it or whatever. You aren't giving them new information, just telling them, basically, that you wouldn't find it surprising if they killed themselves over this.