One eyeball is deeper than the other. Can anything be done to fix this?

It is best to see an oculoplastic specialist to find the cause. Treatment depends on the cause.  There could be also something else causing illusion of sunken eye.

You initially said one eyeball was deeper, but then said both were set deep.  There can be asymmetry from trauma, such as a fracture of the orbit.  There can also be asymmetry from improperly functioning muscles that open the eye.  If both eyes are sunken, it might be simply a matter of your eyelid tissue not having enough fat.  I believe you can be helped, but a complete evaluation would be essential.