DNA repair (DNA damage) foci observed 24 h and later after irradiation are called “residual” in the literature. They are believed to be the repair sites for complex, potentially lethal DNA double strand breaks. However, the features of their post-radiation dose-dependent quantitative changes and their role in the processes of cell death and senescence are still insufficiently studied. For the first time in one work, a simultaneous study of the association of changes in the number of residual foci of key DNA damage response (DDR) proteins (γH2AX, pATM, 53BP1, p-p53), the proportion of caspase-3 positive, LC-3 II autophagic and SA-β-gal senescent cells was carried out 24–72 h after fibroblast irradiation with X-rays at doses of 1–10 Gy. It was shown that with an increase in time after irradiation from 24 h to 72 h, the number of residual foci and the proportion of caspase-3 positive cells decrease, while the proportion of senescent cells, on the contrary, increases. The highest number of autophagic cells was noted 48 h after irradiation. In general, the results obtained provide important information for understanding the dynamics of the development of a dose-dependent cellular response in populations of irradiated fibroblasts.