Question

If you shine a light into a light proof container, then turn off the light, will there still be light/photons inside the container?

Answer 1

If the walls are perfectly reflecting, then yes. The light will continue reflecting around the inside of the box for ever.

But if the walls are black, for example, then the light will become absorbed, but there are still photons in the box called 'black body radiation' which depends upon the temperature of the walls of the box.  

If the walls are partially absorbent, or partially reflecting, the same answer applies but it takes a little longer to reach this equilibrium condition. And this still applies even if the walls have been painted with a colour, so that when illuminated in visible light the walls appear coloured. 

Comments

Just one presision (maybe out of scope): if the reflecting cavity (container) is smaller than the wavelength of the electromagnetic wave, then such a wave may not be excited and maintained in this reflecting cavity. Generally, the container may have a discrete spectrum of the eigenwaves, so there exists the maximum wavelength that may belong to the cavity spectrum.