Delays in achieving polio eradication have led to ongoing risks of poliovirus importations that may cause outbreaks in polio-free countries. Because of the low, but non-zero risk of paralysis with oral poliovirus vaccines (OPVs), countries that achieve and maintain high national routine immunization coverage have increasingly shifted to exclusive use of inactivated poliovirus vaccine (IPV) for all preventive immunizations. However, immunization coverage within countries varies, with under-vaccinated subpopulations potentially able to sustain transmission of imported polioviruses and experience local outbreaks. Due to its cost, ease-of-use, and ability to induce mucosal immunity, using OPV as an outbreak control measure offers a more cost-effective option in countries in which OPV remains in use. However, recent polio outbreaks in IPV-only countries raise questions about whether and when IPV use for outbreak response may fail to stop poliovirus transmission and what consequences may follow from using OPV for outbreak response in these countries. We systematically reviewed the literature to identify modeling studies that explored the use of IPV for outbreak response in IPV-only countries. In addition, applying a model of the 2022 type 2 poliovirus outbreak in New York, we characterized the implications of using different OPV formulations for outbreak response instead of IPV. We also explored the hypothetical scenario of the same outbreak except for type 1 poliovirus instead of type 2. We find that using IPV for outbreak response will likely only stop outbreaks for polioviruses of relatively low transmission potential in countries with very high overall immunization coverage, seasonal transmission dynamics, and only if IPV immunization interventions reach some unvaccinated individuals. Using OPV for outbreak response in IPV-only countries poses substantial risks and challenges that require careful consideration, but may represent an option to consider for some outbreaks in some populations depending on the properties of the available vaccines and coverage attainable.