When I see someone else being embarrassed / humiliated, for example a singer forgetting their words in a concert, I would say something like "I feel embarrassed for them". But is there a better word to describe this feeling?
I would say it's a mix of:
- Empathetic discomfort for someone else's humiliation
- Tension; hope that spectators will be forgiving
- Frustration that I cannot help them
Other scenarios I would feel the same emotion:
- Seeing someone make a presentation, the slides are all out of order, and their face gets red with embarrassment while there's a tense silence in the room.
- Seeing someone make an embarrassing social blunder in front of unforgiving people.
- Seeing a speaker who keeps making a distracting and annoying gesture, and they don't realize that the whole audience is annoyed.
- Seeing someone be taken advantage of, like seeing someone naively and happily accept a terrible offer on a car.
- Seeing a person of strong image (for example the CEO of your company) do something like accidentally leave their webcam on after a conference call, and employees see him/her let out a big burp and pick their nose or something.
In these cases it's important that the audience is not forgiving, even if they don't confront the person about it. The person may or may not know they are being humiliated.
"Pity" as proposed in an answer seems very close, but I think it lacks a few components. I think "pity" has a chronic connotation - that you are referring to the general state of things rather than a specific event.
I think "pity" also depends on the subject suffering, but in my example they are often oblivious.
It could very well be that there is no word for this at all.
NOTE: Some people do not feel the same way I do in this scenario, so you may not think this question makes any sense.