Umm, well without knowing more specifics I can only offer my own experience really- my ex was a heavy social drinker and would be paralytic about 3 times a week. While in that state, he'd humiliate me in public, call me names, ignore me or say things that hurt my feelings.
I didn't deal with it very well, I must admit. I pleaded with him to be nicer, or I left the pub, and on one occassion I punched him because while slaughtered he said he found my flatmate attractive. I've never been much of a drinker so I was sober through most of these occassions.
But, that was a very bad, toxic, messy relationship and at the time I had nobody to turn to and nowhere to go.
Having been through that, and now I'm stronger, I'd now tell the person in question while they're sober what a disgrace they are while drunk, and not put myself in social situations with them. If its a partner and it happens a lot, and they don't change after you've said the above, well then they clearly have a problem and it's time to leave.
But, again, its hard to be more specific to such a general question.