Ellipsis is a linguistic phenomenon characterized by the omission of one or more sentence elements. Solving such a linguistic construction is not a trivial issue in natural language processing since it involves the retrieval of non-overtly expressed verbal material, which might in turn require the model to integrate human-like syntactic and semantic knowledge. In this paper, we explored the issue of how the prototypicality of event participants affects the ability of Language Models (LMs) to handle elliptical sentences and to identify the omitted arguments at different degrees of thematic fit, ranging from highly typical participants to semantically anomalous ones. With this purpose in mind, we built ELLie, the first dataset composed entirely of utterances containing different types of elliptical constructions, and structurally suited for evaluating the effect of argument thematic fit in solving ellipsis and reconstructing the missing element. Our tests demonstrated that the probability scores assigned by the models are higher for typical events than for atypical and impossible ones in different elliptical contexts, confirming the influence of prototypicality of the event participants in interpreting such linguistic structures. Finally, we conducted a retrieval task of the elided verb in the sentence in which the low performance of LMs highlighted a considerable difficulty in reconstructing the correct event