In roughly this order
You do not have to do all of it. Doing the first two is worth more than reading all of it.
1
Understand that it is not only a career problem
A long search is an identity disruption, a financial pressure, a sleep problem and a social withdrawal at the same time. The person is probably experiencing more shame than they are showing, and quite possibly performing more confidence than they feel in order to protect you.
2
Ask specific questions instead of general ones
“How did the conversation with Sam go?” lands completely differently from “how's the search going?”. The specific question signals real attention. The general one invites a performance of being fine, which is what most people will give you.
3
Offer help attached to a task
“I could look over that message if you want another pair of eyes” is usable. “Let me know if I can do anything” requires them to identify a need, ask for it and feel indebted, which is three obstacles when they have no spare capacity.
4
Invite them to exist outside the search
A walk, a meal, a film, a football match. Something with no relationship to employment. The invitation is valuable even when it is declined, because it says the person is still a person to you.
5
Avoid three things that feel supportive and are not
Enthusiasm about opportunities that have not materialised, which lands as pressure. Comparisons to people who found something quickly, which closes the conversation. And solutions offered before the feelings have been heard — “that sounds really hard” first, every time.
6
Know what the serious signals look like
Persistent low mood beyond two weeks, complete withdrawal, inability to manage daily life, or any suggestion that others would be better off without them. If you are worried about their safety, ask directly and calmly — a review of the studies that tested this found no evidence that asking plants the idea (Dazzi et al., Psychological Medicine, 2014) — and stay with them.
7
Get some support of your own
Supporting someone through months of this is heavy, and carrying all of it inside the relationship is too much to ask of either of you. Samaritans will talk to you about someone you are worried about, not only to the person themselves.
The three topic pages most worth your time from here
If you work in recruitment or hiring rather than knowing someone personally, there is a page for that too — hiring processes have consequences outside the hiring process.