The word "degrace" is a somewhat uncommon and archaic term. It refers to a state of disgrace or disrepute, usually associated with a public figure whose reputation has been tarnished. Synonyms for this word include shame, dishonor, infamy, and ignominy. Other terms that could be used to describe a similar state of disgrace include humiliation, embarrassment, and mortification. In a more nuanced context, you might also consider using words like stigmatization or social ostracism to describe the lasting impact of a particular disgraceful act or event. Regardless of the specific word chosen, all of these synonyms suggest a loss of respect or dignity that can be difficult to recover from, particularly in a public setting.