Exciton states in lead selenide (PbSe) and lead sulfide (PbS) quantum dots have been studied extensively. However, relatively less attention has been paid to the states within the quantum dot bandgap. Our experimental results have revealed a single in-gap state which bears confinement dependence yet cannot be explained by dark exciton theory, nor is it a trap state related to quantum dot surface defects as previously observed. A detailed analysis of the temperature dependence of photoluminescence, Stokes shift, absorption and photoinduced absorption indicates the unconventional GS is a new state of a trapped exciton in a QD film. With appropriate design engineering, these trapped excitons might be harvested in solar cells and other optoelectronic devices.