For the second -- it is on the manager to know enough about the reasons affecting their report's performance to be able to adapt before the team underperforms. (and it is on the report to surface that information quickly so that the team isn't compromised)
I once worked with a manager who would always ask for details like "oh you have a headache? Do you have a fever?" While I think his intentions were good, and that he just wanted to show concern and even offer support or advice, I always found the questions incredibly invasive and a violation of my privacy.
My team knows that I will always listen if an employee wants to share details of their personal lives (upto anything that crosses the line of appropriatness for work), but I would never pry.
So, in this example, I would never know an employee is struggling with a personal issue, unless they broached the subject with me.
Personally, if I'm sick, the last think I want to do is communicate with my manager - it means you have to be careful, you never know if they're digging, or 'professional but not exactly sincere empathy' etc..
'Adult Professionals' shouldn't need to be coddled. If you're sick you're sick and that's that.
If you have something that's a 'big deal' then you have that in a conversation in which the managers emotional response one would expect is empathy but beyond that it's a matter of 'how to work around it'.
'Trust' is a multifaceted thing, I generally do not trust that people will do their jobs well at the outset, until I've seen evidence of that, but as far as those kinds of workplace issues I definitely 'trust by default'. People get sick and that's that.
And then have a lot of tolerance because we are all a little odd in our own ways and it's just easier not to get caught up in stuff.
If I didn't have such a relation with my manager I'd be looking for a job. If he doesn't look out for me when I'm sick he will probably not look out for me professionally either.
Second point, sure. That's the ideal. But it's not always going to happen, and you need to be able to deal with that situation to be a well rounded manager and leader. IMO.
You can still try to find out what causes their behavior (by showing interests into their perspective) and may be able to help them and therefore the team.
- If they have a different perspective, it should be helpful to listen to their perspective.
- If they have a bad day, it will go away.
- If they have family or health problems, you might not want know the details, but simply knowing that a person is going through a difficult time might give you enough information to know how to improve the situation.
Even if you are not the cause of the situation, you might still be able to improve it as a manager.
If you haven't built trust with every person on your team, that doesn't make you a shitty manager. The more people you can work with and trust, the more effective you may be as a manager, but don't let a counterexample serve as proof positive that you suck. Trust is a two way street.
Sometimes people underperform for other reasons that have nothing to do with you. They may have a different perspective, or they may just be having a bad day. Or they may have family or health problems affecting them. Or, they may actually just no longer care or not be good at their job.