if an aggregate function returns a null with min or max, then it, and by extension, your database, are both broken.
aggregate functions, by the SQL spec, should not consider NULLS in their operation.
I.e. if you have three rows, with 0,1 and NULL stored and ask for AVG you should get 0.5, since the NULL shouldn't count on the top or the bottom of the average equation, but should be thrown out.
On the other hand, if it's a string, and you use min, and the string if '', you might get an empty string back, which isn't the same thing as a null.