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Thank you for your answers and comments. To sum up, "loss of face" denotes loss of personal dignity, standing and respect in the eyes of others, implying mild humiliation, social degradation or embarrassment.
Now I am wondering which are the phrases or sayings related to this. The expression "to have egg on your face", for instance, might be used to express embarrassment, but not in the context of Auster's fragment. Perhaps this is more colloquial than "loss of face". Is there any other more suitable?