I don't think that should be the way things happen. At the very least, we should make an attempt to see if people in a state of being down want to talk about it with us. In my life, I've chosen to risk being rebuffed for the chance that the people I see being sad need somebody to talk to. Does that make sense? It would be better to be rejected while trying than to never try and have wasted a chance.
Here's a poem that kind of addresses that topic:
Nobody knows who I am within;
What kinds of doubt and fear reside
Beneath my actions, or their origin.
Inside, so many dreams and wishes died.
If opportunity does come,
What will happen?
Will I go numb?
Or will I take it? What then?
In my life, and I’m a fool.
Why can’t I turn this around?
Will I always be lost, and never found?
I can’t count the cost of happiness;
Conquer the darkness that leaves me with less.
People look, but never address the real problems
Or the aloneness that condemns
Me to live this life.
Inside, there’s a knife
Cutting deeper and deeper,
And a road, getting steep and still steeper.