The goal of this paper is to explore the demographic evolution of the Coronavirus SARS-CoV-2 deaths and cases in the state of Paraná, Brazil. We focus on changes in the age-pattern of cases and deaths attributed to the COVID-19. Paraná is an interesting case of study in Brazil due to several aspects. First, it is one of the most developed states of the country. Second, the population growth rate is rapidly approaching zero growth, with an observed average growth rate of 0.78 percent per year in the decade 2010/2020, and of 0.28 percent per year in the period 2030/2040. Third, Parana has an older population age-structure than that of the whole country. Finally, although the state government pushed for earlier Non-Pharmaceutical Interventions to control the pandemic, data shows that they only took effect in the very late stages. Taken together, we claim that these aspects created a very particular setting, in which changes over time in the age-structure of the deaths attributed to COVID-19 could be observed: in the beginning of the pandemic, the age-structure of the deaths was concentrated among the elderly. As the pandemic unfolds, deaths were spreading over younger ages. Finally, we speculate on mechanisms behind the changes in the age structure of the COVID-19 deaths in Paraná.