A possible explanation is proposed for the observation that late-type stars falling in a certain region of the H-R diagram exhibit no X-ray emission and hence appear not to have coronae. It is argued that, due to the low surface gravity of these stars, the hot X-ray emitting loops in their atmospheres simply become cool and emit at longer wavelengths. This argument is demonstrated quantitatively by considering the effect on a typical solar loop of scaling it up to parameters appropriate to a supergiant.