A Failure To Rescue can be defined as a clinical deterioration and/or functional failure of a patient, which could have been prevented by early detection and appropriate intervention. It represents a major challenge in clinical practice, often arising from complex care processes where multifactorial variables are not fully integrated. To address this issue, this Teaching Case explores how Process Mining and Predictive Process Monitoring techniques can be applied to hospital data to identify critical pathways, predict adverse outcomes, and ultimately reduce the FTR rate. The article presents a comprehensive Teaching Case that includes both the case study itself, along with the questions and tasks posed to students, and a complementary link to the Teaching Notes, which serve as a support resource for instructors in guiding the implementation of the case in educational contexts. The Teaching Case is based on real, pseudoanonymized clinical data from a medium-sized hospital and is aimed at postgraduate students in disciplines such as Artificial Intelligence, Business Process Management, or Medical Informatics. It enables learners to develop core BPM competencies in Process Discovery, Conformance Checking, Predictive Process Monitoring, and process redesign within a critical healthcare context.