Recovery of resources, in particular, metals, from waste flows is widely seen as a prioritized option to reduce their potential supply constraints in the future. The current waste electrical and electronic equipment (WEEE) treatment system is more focused on bulk metals, where the recycling rate of specialty metals, such as rare earths, is negligible compared to their increasing use in modern products, such as electronics. This study investigates the challenges in recovering these resources in the existing WEEE treatment system. It is illustrated by following the material flows of resources in a conventional WEEE treatment plant in Denmark. Computer hard disk drives (HDDs) containing neodymium–iron–boron (NdFeB) magnets were selected as the case product for this experiment. The resulting output fractions were tracked until their final treatment in order to estimate the recovery potential of rare earth elements (REEs) and other resources contained in HDDs. The results further show that out of the 244 kg of HDDs treated, 212 kg comprising mainly of aluminum and steel can be finally recovered from the metallurgic process. The results further demonstrate the complete loss of REEs in the existing shredding-based WEEE treatment processes. Dismantling and separate processing of NdFeB magnets from their end-use products can be a more preferred option over shredding. However, it remains a technological and logistic challenge for the existing system.