Super-resolution optical fluctuation imaging overcomes the diffraction limit by analyzing fluctuations in the fluorophore emission. A key assumption of the imaging is that the fluorophores are independent, though this is invalidated in the presence of photodestruction. In this work, we evaluate the effect of photodestruction on SOFI imaging using theoretical considerations and computer simulations. We find that photodestruction gives rise to an additional signal that does not present an easily-interpretable view of the sample structure. This additional signal is strong and the resulting images typically exhibit less noise. Accordingly, these images may be mis-interpreted as being more visually pleasing or more informative. To address this uncertainty, we develop a procedure that can robustly estimate to what extent any particular experiment is affected by photodestruction. We also develop a detailed assessment methodology and use it to evaluate the performance of several correction algorithms. We identify two approaches that can correct for the presence of even strong photodestruction, one of which can be implemented directly in the SOFI calculation software.