The pervasive and growing illiberal movement is, perhaps, the greatest global challenge to liberal democracy today. Scholars argue that domestic and international crises have played an important role in perpetuating illiberalism among leaders and growing its support among their populace. In this paper, we set out a research agenda for the systematic study of illiberal policy frames (IPFs). In illustrating the potential of the concept and its operationalisation, we analyse how legislative politicians have used policy crises to communicate their policy ideas through IPFs. First, we define and measure illiberal frames in four countries (Austria, Germany, Hungary and the United States) for two policy issues (migration and COVID-19) using a novel IPF codebook and state-of-the-art large language models. Second, we assess the extent to which the use of these frames is sensitive to exogenous policy crises. Our findings suggest that the usage of illiberal political frames does not closely track the pertinent policy crisis metrics, such as the number of asylum seekers (for migration) or casualties (for COVID-19). Narratives show no relation to markers of the underlying policy crises, which points to a political strategy based on continued fear-mongering rather than crisis exploitation.