The reconstruction of very inclined air showers is a new challenge for next-generation radio experiments such as the AugerPrime radio upgrade, BEACON, and GRAND, which focus on the detection of ultra-high-energy particles. To tackle it, we study the electromagnetic particle content of very inclined air showers, which has scarcely been studied so far. The features of the radio signals emitted by very inclined air showers are significantly different from those of vertical ones; in particular, they present a drastic drop of the geomagnetic emission amplitude. Using the simulation tools CORSIKA and CoREAS, and analytical modeling, we explore the energy range of the particles that contribute most to the radio emission, quantify their lateral extent, and estimate the atmospheric depth at which the radio emission is strongest. We find that the distribution of the electromagnetic component in very inclined air showers has characteristic features that could impact the reconstruction strategies of next-generation radio-detection experiments.