If you are ill, you are ill. There's no choice about it. So in normal usage 'he is ill' would be the only option. But informally, and in a joking/mocking way, someone might say 'He is "being ill" '; hearing the unusual use of the progressive, the hearer 'sees' the quotation marks and concludes 'Aha, So-and-so's just being a hypochondriac, as usual.'
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