As always, in this kind of situation, one should not put pressure on someone else. I faced the same situation with people I know/knew (and hadn't seen for a long time). A quick search will explain what "not to say/do", so I'll focus on the "what to say" part.
When you go through a rough time, like a personal loss, or a personal or professional tsunami, you don't want people to add a single straw on your burden. In this case, I don't tell or ask people anything, I just let them know I still exist. I had once news from former colleagues, and we had this chit-chat-workplace-gossip when you share funny (or not...) memories, remind each other some weird situation, or just share another rant about X/Y/Z. Ya'know, the good ol'times...
At one time, one person mentioned something similar to what you tell us. We spent a few minutes about this topic and moved on to another one...
What I did, back home, was to send a mail to the person. I roughly told her what happened: the meeting, the good old times 1, the lunch/drink, the laughs 2. And I told her that it reminded me of the time we worked together, and 'this funny thing that made her smile' 3.
Then a few banalities, some unimportant news about me (like work, because we shared it too). And now, the important part, "hidden" at the end: "I'll be glad to hear from you if you [ feel like mailing back / have time to mail back ]. Or even a drink, if you drop by "place you both know and used to go to after work" one of these days". Not more. Knock on the door, and wait for an answer. In any case, don't mention the topic of what she's going through. Neutral and happy if possible.
You can offer support only if it's accepted and not forced, so, it has to come from the person. They may (or may not) want to talk about their emotional status, so they'll open up if they feel like it. To you or to someone else. Be there and just listen, you'll know more than by talking and asking.
Doing this, you let the person know you're "still alive", and realize they're not alone, that some people still like them, or care for them. Sometimes, just talking a little is enough and warms you up. In my case, we didn't have a chance to meet, but it was her choice. But she answered, and we talked by mail, telling stories, recalling the workplace, and talking about the present, and she even called me once. Small chit-chat, but I could hear a normal tone, not depressed.
Then back to routine. But I could feel that she had enjoyed our small talks (one or two emails a week for a few weeks). When emails stopped, I didn't bother her. We had moved on.
It's up to the person you'll talk to, and the relationship you had, so the result will or can probably differ. My advice is to keep in mind that it has to be her choice to answer or not. And that you should only be positive about the past, maybe ask about the present (pleasantries, not more), but be very lighthearted. Bring back smiles, not sadness or painfull memories.
1 & 2 & 3 - note: positive things only.