com besiege 1 : to surround with armed forces 2 a : to press with requests : importune b : to cause worry or distress to : beset <doubts besieged him> stroke 5 : sudden diminution or loss of consciousness, sensation, and voluntary motion caused by rupture or obstruction (as by a clot) of a blood vessel of the brain -called also apoplexy , brain attack, cerebrovascular accident Hence, besieged by apoplexy = suffering from the effects of having had a stroke, perhaps unable to speak or walk, for example. The word apoplexy is very rare in modern English. The modern term is stroke .
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MFGI've heard of this once before. It is "besieged by apoplexy," and it's a grandiloquent way of saying that one is so mad that s/he is on the verge of having a stroke.That works for me as a figurative use.