I do have something to share. I would ask the following:

1. Is he getting well with his advisor?

2. Does he have a daily routine (i.e wake up at 8AM everyday, preparing for teaching, going to gym at 11AM, reading papers from 1PM, attending weekly seminar at 3PM, etc). This can be crucial to get someone out of the state of depression.

3. Does he have potential plans after the PhD (with or without the degree)?

If the answers are No, I would suggest taking some concrete steps now (switch to a new advisor, form a daily life routine, consider a Plan $B$ or even Plan $Z$ in case academia does not work for him).

In case he still love doing research, I would encourage him/her talk to some mathematican in industry but still actively doing research to have a better sense how to achieve this. If I recall correctly, Yakov Eliashberg, Vladmir Berkovich and Jeffrey Lagarias all worked at industry at some point, not to mention street names like Yitang Zhang.

I do have something to share. I would ask the following:

1. Is he getting well with his advisor?

2. Does he have a daily routine (i.e wake up at 8AM everyday, preparing for teaching, going to gym at 11AM, reading papers from 1PM, attending weekly seminar at 3PM, etc). This can be crucial to get someone out of the state of depression.

3. Does he have potential plans after the PhD (with or without the degree)?

If the answers are No, I would suggest taking some concrete steps now (switch to a new advisor, form a daily life routine, consider a Plan $B$ or even Plan $Z$ in case academia does not work for him).

In case he still loves doing research, I would encourage him/her talk to some mathematican in industry but still actively doing research to have a better sense how to achieve this. If I recall correctly, Yakov Eliashberg, Vladmir Berkovich and Jeffrey Lagarias all worked at industry at some point, not to mention street names like Yitang Zhang.