Background: Older people with dementia are particularly at risk of COVID-19; however, relatively little is known about the indirect impact of the pandemic on the lives of those living with, and/or caring for someone with, dementia. Objectives: The aim of this study was to investigate the experiences of people with dementia and informal carers during the closure of available social and medical services in Poland during the COVID-19 pandemic. Methods: A qualitative thematic analysis of semi-structured interviews with people with dementia (n = 5) and informal carers (n = 21) was performed between June and August 2020 after the first wave of COVID-19 in Poland. Findings: Three overarching themes were identified: (1) care re-organization; (2) psychological responses; (3) emerging needs. The factor underlying all these elements was reliance on other people. Social support and engagement are vital to the ongoing health and well-being of people living with dementia and their informal carers. Services need to be strengthened to provide ongoing provision to those living with dementia to reach pre-pandemic levels, if not better. Conclusions: Within the post-pandemic environment, people with dementia and their informal carers need reassurance that they can rely on external institutional and social support able to meet their needs.