Homology search is a means through which DNA double-strand breaks (DSBs) explore the genome for sequences that enable error-free repair, known as homologous recombination. A better understanding of this search process is fundamental to the relationship between higher-order chromosome organization and DNA damage. Here, we use an entropic bead-spring polymer chain model to simulate the spatiotemporal dynamics of the yeast genome during interphase. The chromosome is organized by transient and dynamic cross-links representing structural maintenance of chromosome (SMC) complexes. DNA damage is modeled as a break in the bead-spring chain, coupled with a removal of crosslinks from beads proximal to the break site. We show that the removal of cross-links drives the exploration of genomic space by the damaged ends, while rates and densities of intact dynamic crosslinking have only a minor role. Local depletion of SMC cross-links proximal to the break site enables the damaged segment to escape the chromosome territory and enhances its ability to explore the genome. Our study reveals a foundational principle by which DSBs can encounter distant regions of sequence homology.