One promising strategy to alleviate aging symptoms is the treatment with senolytics that is compounds which selectively eliminate senescent cells. Some therapies aim to reduce symptoms of cellular senescence without senescent cell eradication (senomorphic activity). However, senotherapies raise many questions concerning the selectivity, safety and efficiency of senolitic drugs. A vital question is how the senolytic compounds affect young proliferating cells. In our study, we checked the impact of quercetin and dasatinib (D + Q), one of the promising drug mixtures of drugs, on chromatin structure in young and senescent cells. We analyzed the effect of a single and triple drug treatment on vascular smooth muscle cells. We have shown that D + Q impacts the chromatin in both young and senescent cells. In senescent cells, D + Q caused some symptoms of chromatin “rejuvenation” but in young cells some changes characteristic of senescent cells were observed. The alterations in young cells appeared only transiently and chromatin returned to the initial state after 24 h of recovery. The complexity of chromatin staining and nucleus morphology evaluation indicated that a triple treatment makes senescent cells more similar to the young ones than a single treatment. However, the analysis of senescence markers suggested that a single treatment with D + Q caused slightly less pronounced senescence characteristics and was more efficient in alleviating the features of senescence than a triple treatment. It is still an open question whether the alterations caused by D + Q are beneficial or harmful in the long term; however, so far, it can be concluded that the effects depend on cell type and the physiological context.