Earlier systematic experimental studies of bursting soap films by McEntee & Mysels (J. Phys. Chem., vol. 73, 1969, pp. 3018–3028) revealed the existence of a precursor shock wave preceding the expanding hole in a punctured film, with a disturbed region of shrinking film material in between known as the ‘aureole’. In the present work we report and interpret new phenomena associated with the aureole – the formation of folds on the surface of soap films. In search of the theoretical explanation of the experimentally identified conditions under which the folds appear, we establish that they correspond to catastrophes of collapsing soap films.