Loss of one species in an ecosystem can trigger extinctions of other dependent species. For instance, specialist predators will go extinct following the loss of their only prey unless they can change their diet. It has therefore been suggested that an ability of consumers to rewire to novel prey should mitigate the consequences of species loss by reducing the risk of cascading extinction. Using a new modelling approach on natural and computer-generated food webs we find that, on the contrary, rewiring often aggravates the effects of species loss. This is because rewiring can lead to overexploitation of resources, which eventually causes extinction cascades. Such a scenario is particularly likely if prey species cannot escape predation when rare and if predators are efficient in exploiting novel prey. Indeed, rewiring is a two-edged sword; it might be advantageous for individual predators in the short term, yet harmful for long-term system persistence.