From Middle English bifallinge, equivalent to befall + -ing.

befalling (plural befallings)

1. A happening; occurrence; chance; event.

1. Present participle and gerund of befall

befalling

1. (archaic) Appertaining; appropriate; fitting.
   • 1564 February, Erasmus, “The Saiynges of Antigonus the Firste Kyng of the Macedonians”, in Nicolas Udall [i.e., Nicholas Udall], transl., Apophthegmes, that is to Saie, Prompte, Quicke, Wittie and Sentẽcious Saiynges, […], London: […] Ihon Kingston, →OCLC ↗, book II, folio 155, recto ↗, paragraph 11, marginal note:

     Bountie & largeſſe is befalling for kynges.