IMPORTANCE: Opioid-related overdose accounts for almost 80 000 deaths annually across the US. People who use drugs leaving jails are at particularly high risk for opioid-related overdose and may benefit from take-home naloxone (THN) distribution. OBJECTIVE: To estimate the population impact of THN distribution at jail release to reverse opioid-related overdose among people with opioid use disorders. DESIGN, SETTING, AND PARTICIPANTS: This study developed the agent-based Justice-Community Circulation Model (JCCM) to model a synthetic population of individuals with and without a history of opioid use. Epidemiological data from 2014 to 2020 for Cook County, Illinois, were used to identify parameters pertinent to the synthetic population. Twenty-seven experimental scenarios were examined to capture diverse strategies of THN distribution and use. Sensitivity analysis was performed to identify critical mediating and moderating variables associated with population impact and a proxy metric for cost-effectiveness (ie, the direct costs of THN kits distributed per death averted). Data were analyzed between February 2022 and March 2024. INTERVENTION: Modeled interventions included 3 THN distribution channels: community facilities and practitioners; jail, at release; and social network or peers of persons released from jail. MAIN OUTCOMES AND MEASURES: The primary outcome was the percentage of opioid-related overdose deaths averted with THN in the modeled population relative to a baseline scenario with no intervention. RESULTS: Take-home naloxone distribution at jail release had the highest median (IQR) percentage of averted deaths at 11.70% (6.57%-15.75%). The probability of bystander presence at an opioid overdose showed the greatest proportional contribution (27.15%) to the variance in deaths averted in persons released from jail. The estimated costs of distributed THN kits were less than $15 000 per averted death in all 27 scenarios. CONCLUSIONS AND RELEVANCE: This study found that THN distribution at jail release is an economical and feasible approach to substantially reducing opioid-related overdose mortality. Training and preparation of proficient and willing bystanders are central factors in reaching the full potential of this intervention.