My general approach towards anyone really, is to provide a safe space for them to come if they wish, to let them know I'm there for them if they need, but I really don't approach them much at all. I like to check in on occasion with a simple "how are you doing?" but if they don't respond with much I leave it at that. But checking in like that, also serves to keep that metaphorical, and emotional door open, should they wish to step in at any time.
I've gotten plenty of flak from more emotionally expressive types because of this, particularly when growing up, and certainly, when my dad died. That was a horrible experience as I not only had to put up with that, but contend with my own emotions of the situation at the time. I've had friends complain to me asking why I don't care more. But, all of this is a misunderstanding of course, as I DO care for others. Quite a bit actually. It's just that I respect their space to grieve, to feel pain, to endure. It's how I prefer to be treated most often, to be left alone, so I take that approach with others.
If I sense a person is going downhill and no longer merely "feeling" but getting into more dangerous territory, that's when I more actively extend my hand to help them out. There's never a hard-defined rule or approach though, as each person responds differently and you just have to feel them out. Approach them in a way that feels right at the time.
With this INTJ friend of yours, perhaps there are other ways you can be with them and to support them. Support doesn't always come in the way of emotions.
