But the 'true' root of Ereignis is not actually eigen but Augen, 'eye'.
It therefore has important links with the discussion of the Augenblick, 'the blink of an eye', or 'moment', throughout Heidegger's work, but especially in Being and Time and the Nietzsche lectures. Just as if The Ereignis would happen all of a sudden, in the bink of an eye, suddenly. Unexpected. And Heidegger seems to be making simultaneous use of its 'true' and apparent etymologies.
Heidegger is therefore playing with a number of meanings at once, which are well preserved in the English'propriation' and related words, with the senses of proper, property, peculiarity, suitability, own, owning, ownership, belonging, appropriation.
But not preserved at all with the sense of the unexpected...