I would push back on this bizarre request. That's exactly what NULL is for in SQL, to denote a missing or inapplicable value in a column.
Is the requester experiencing grief over SQL logic with NULL?
edit: Okay, I've read your reply with the extra detail about this job assignment (btw, generally you should edit your original question instead of posting more information in an answer).
You'll have to declare all columns as NOT NULL and designate a special value in the domain of that column's data type to signify "no value." The appropriate value to choose might be different on a case by case basis, i.e. zero may signify nothing in a person_age column, but it might have significance in an items_in_stock column.
You should document the no-value value for each column. But I suppose they don't believe in documentation either. :-(