Cancer is caused by the lifetime accumulation of multiple somatic deformations of the genome and epigenome. At a very low rate, mistakes occur during genomic replication (e.g., mutations or modified epigenetic marks). Long-lived species, such as elephants, are suggested to have evolved mechanisms to slow down the cancer progression. Recently, the life span of companion dogs has increased considerably than before, owing to the improvement of their environment, which has led to an increase in the fraction of companion dogs developing cancer. These findings suggest that short-term responses of cancer risk to longevity differ from long-term responses. In this study, to clarify the situation, we used a simple multi-step model for cancer. The rates of events leading to malignant cancer are assumed to be proportional to those of genomic replication error. Perfect removal of replication error requires a large cost, resulting in the evolution of a positive rate of genomic replication error. The analysis of the model revealed: that, when the environment suddenly becomes benign, the relative importance of cancer enhances, although the age-dependent cancer risk remains unchanged. However, in the long run, the genomic error rate evolves to become smaller and mitigates the cancer risk.