Anchor Light Can You Install A Ordinary Light Fixture Onto A Recessed Lighting Fixture Can?

Can you install a ordinary light fixture onto a recessed lighting fixture can? - anchor light

I installed a house with recessed lights and you want a lamp that a normal person is now installing recessed lighting system. Can I use an adapter from one species to the deeper lighting that is anchored and wired and use appropriate lighting the lamp luminaires external fixation? Starting from scratch, I cut the roof to remove the lamp assembly and re-anchor the new lamp that resembles a devil of a time when greatness. Thank you!