You're probably referring to the case of a city fire department that offers service to its (tax-paying) residents, but charges an annual fee for residents outside the city limits. When one of those houses in unincorporated land is on fire but hasn't paid their fee, then - once they have ensured no lives are at risk - they choose to let it burn.
http://www.firehouse.com/news/10472820/tennessee-fire-depart...