do you think people who cant sing can be taught to?

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i'm talking about the worst like american idol in the auditions, when they sound tone deaf. if they had the commitment and the aptitude do you think they could sound in the least angelic? do you know someone who sounded absolutely terrible, but after they had quite a few singing lessons their singing improved. by improved, i mean by alot. is it possible? i have never heard of anybody who couldnt sing being taught to sing and sounding better for it. i usually asks questions that i know the answer to but like to know peoples views on that particular discussion, but this one i dont have a clue on. even if you dont know the answer like me, please comment on it as i would like to know what other people think, as to wether someone who is tone deaf could be taught to sing.