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If a person with their top off still looks like their sternum has collapsed, it could be that they are suffering from a medical condition called Pectus Excavatum. The term is Latin, and means roughly 'scooped chest'. The typical form is of a 'bird-bath' depression in the sternum, possibly making the torso very narrow in the centre, as the sternum approaches the spine. Although there are several causes of this minor deformity, it can be an important indicator of Marfan Syndrome. Other signs to watch for are an abnormally high palate, an arm-span exceeding body height, and long fingers and toes. Of course, none of these factors, separately or together, is a sure test for the condition.

Source: Written from memory, as my brother has Pectus Excavatum and other Marfan indicators, but apparently not the debilities associated with the condition.