Addiction problems impact not only the persons with these problems but also family members. This study aims to examine the impact of the COVID-19 pandemic on stress, strain on health, study experiences, coping strategies, and access to support of students with relatives with addiction problems. Thirty students, aged 18–30 years, from a University of Applied Sciences in the Netherlands participated in a three-year qualitative longitudinal interview study. One round of individual semi-structured interviews was conducted before the COVID-19 pandemic, and three during the COVID-19 pandemic. Directed Content Analysis was applied, using the Stress-Strain-Information-Coping-Support-model. Four major themes were identified: (1) Increase in stress and strain; (2) Decrease in stress and strain; (3) Coping strategies, and (4) Access to social, professional, and educational support. Before the pandemic, most participants had health problems, especially mental health problems, including problems with their own substance use. Some had study delay. Analysis revealed that during the pandemic, most participants experienced an increase in these problems. This appeared to be related to their living situation: An increase in violence and relapse of relatives increased stress, especially for those living with their relatives. The coping strategies ‘standing up’ or ‘putting up’, and a decrease in support—social, professional, and educational—also contributed to stress. A few participants experienced less health problems and study problems. This was related to diminishing addiction problems of relatives, less social pressure, available help, and the coping strategy ‘withdrawing’. Withdrawing was much easier for participants who did not live with their relatives with addiction problems. It is recommended to keep schools and universities open during pandemics, offering a safe haven for students at risk in the home situation.