This is one of those things that shouldn’t need to be said, but needs to be said - People are more important than goals.
Obviously, only the worst of the worst manager would demand that someone finish an assignment from a hospital bed (don’t laugh - I bet someone has done it).
Don’t get caught up on the major cases - the minor cases too. Everyone makes sacrifices for work - misses a family event once in a while, works late and misses dinner, etc. Managers need to be aware of the little things that give the impression that the goal matters more. What are some of these things:
Passive-aggressive threats - “You want to leave early for your daughter’s softball game? Sure, I guess others won’t mind picking up the slack for you."
Modeling poor behavior - don’t place your goals ahead of your non-professional life and let them see it. I always made it a point to tell my team if I would be leaving early or coming in late because of a family obligation. It was a nice communication device for me and it showed where I placed importance.
Non-verbal signs. Some managers will do things like heavy sighs or eye rolling. It may be meant as negative feedback to the employee (not real negative feedback because it doesn’t follow the process). It may also not mean anything and be innocent. Be cautious because your team will pay very close attention to your non-verbal clues.
As a caveat: In rare cases where goals are truly critical, ask the employee to sacrifice and do it in a way that really gives them a real option. If you’ve developed good relationships, most of the time you won’t have to ask because they will want to go above and beyond for you or they will do it because you have been a great manager.