Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks, this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight into the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps toward understanding more complex network splitting scenarios.