We investigate a hypothesis that energy accumulation and the subsequent release in NaI(Tl) may lead to pulse-like events in the few-keV energy regime, a phenomenon suggested by the crystal manufacturing company Saint-Gobain, who provided the crystals for DAMA-LIBRA. While we observed delayed long-lasting light emission in a 3" NaI(Tl) crystal after exposing it to UV light, the delayed light consists primarily of single photons that are uncorrelated with each other. We also observe delayed light emission in NaI(Tl) following gamma radiation and large ionization events like cosmic-ray muons. We found that irradiating the crystal with red light after UV exposure significantly suppressed delayed photon emissions.