During nursing education, few practical hours are devoted to comprehensively preparing students to care for a dying patient. Contact with a dying patient is a key element of the job of every working nurse in the profession. Therefore, it is necessary to properly prepare nurses to care for a dying patient. This study aimed to assess the professional competence of nurses in caring for a dying patient and the factors that affect this preparation. This study involved 223 nurses during master’s degree in nursing at the Medical University of Warsaw, receiving either full-time education (group I, N = 121) or hybrid education (group II, N = 102). The study used the FATCOD-BP ((Frommelt Attitudes Toward the Care Of the Dying scale Form B, Polish version)) questionnaire (Cronbach’s alpha 0.75), an original questionnaire containing questions about feelings experienced during the SARS-CoV-2 virus pandemic and sociodemographic questions. FATCOD-BP for all groups was below average regarding caring for a dying patient (M = 109, SD = 11.68). Nurses pursuing full-time education were better prepared to care for a dying patient than were nurses pursuing hybrid education. Nurses who exhibited fear of their own deaths had a lower subjective level of preparation for caring for a dying patient. (1) Nurses are not sufficiently prepared to care for a dying patient. (2) The training of nurses should be provided in the form of in-patient education, and the methods of training should be modified by increasing the number of hours of practical and theoretical instruction in palliative care for a dying patient.