This article presents a crosslinguistic study of the association of event-oriented modal categories, particularly the potential and the necessitive, with non-canonical case marking of the subject and voice-related constructions. It is estimated that in at least a quarter of the languages of the world such an association exists. Voice-related constructions are much more strongly associated with the potential than with the necessitive, and the source constructions are overwhelmingly passive and spontaneous voice. Accordingly, a grammaticalization path from passive and spontaneous to potential can be posited. Furthermore, it was found that the expression of modality with non-canonical case marking patterns often originates in, or is associated with, possessive constructions, usually resulting in necessitive constructions. Possible motivations and contexts for the development of the constructions under investigation are suggested.