Transcription machinery ultimately depends on the temporal formation of protein-DNA complexes. Recent experimental studies demonstrate that residence time (i.e., inverse off-rate) of a transcription factor protein can be a contributor to the functional diversity of the protein. In the meantime, single-molecule experiments showed that the off-rates of a wide array of DNA-binding proteins accelerate as the bulk concentration of the protein increases via a concentration-dependent mechanism (i.e., facilitated dissociation, FD). In this study, inspired by the previous single-molecule studies on the factor for inversion stimulation (Fis) protein of E. coli, which is a dual-purpose protein with a diverse functionality, we model the unbinding of Fis from specific bindings sites along a high-molecular-weight circular DNA in a cylindrical structure mimicking the cellular confinement of chromosome. Our simulations show that FD of Fis can well occur in confinement at physiological concentrations. Particularly, when nutrient-rich conditions are emulated with Fis concentrations around micromolar levels, the off-rates increase one order of magnitude compared to the lower Fis levels. However, Fis significantly changes the chromosome structure at higher concentrations by forming dense protein clusters bridging specific sites and juxtaposing remote DNA segments. As a result, at the physiologically observed maximum levels of Fis, the off-rates significantly slow down. Overall, our results indicate that cellular-concentration levels of a structural DNA-binding protein is intermingled with the genome architecture and DNA residence times, thereby providing a basis for understanding the complex effects of dynamic protein-DNA interactions on gene regulation.