The death rate from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in 2022 was lower than the death rate in 2021, when the infection rate increased. Hybrid immunity provided by a combination of vaccination and infection, including asymptomatic infection, may confer effective protection against death. We explored the combined effect of asymptomatic infection and hybrid immunity by studying T-cell and antibody responses against SARS-CoV-2 among individuals treated in home health care services 6 months after SARS-CoV-2 exposure. Asymptomatic SARS-CoV-2 infection was demonstrated in 24.4% of close contacts. The levels of immunity were not different between patients and close contacts. Anti-RBD IgG against SARS-CoV-2 increased in a dose-dependent manner with the number of vaccine doses. Interestingly, the T-cell response decreased soon after a booster dose of vaccine. Asymptomatic SARS-CoV-2 infection could not enhance immunity against SARS-CoV-2 among vaccinated close contacts. Full vaccination was crucial to provide hybrid immunity. However, when designing vaccine strategies, T-cell exhaustion after multiple vaccinations should be considered.