To come as something additional or extraneous; to occur with reference or relation to something else; to happen upon or after something else; to be added; to take place; to happen.
a numbness, an occasional stupor, fell upon my mind even in the midst of my terrors, until sleep at last supervened and in my sea-tossed coracle I lay and dreamed of home and the old Admiral Benbow.
Robert Louis Stevenson. Treasure Island (1882)
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by becoming stabilised, so consistently that the strain of waiting having hardly time to relax before a fresh reason for waiting supervened, there was no longer a single minute in the day in which I was not in that state of anxiety which it is so difficult to bear even for an hour.
Marcel Proust. In Search of Lost Time [volume 2]
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Hubbard, I am informed, is suffering from an attack of stomach poisoning, which has supervened during the night. He says that he does not know what can have caused it.