I'd say stiff adverbially modifies set in OP's context, but that may be just a matter of opinion. Compare these two written instances...
1: the bird goes gaily on, and with stiff-set wings sails downward
2: A strong-framed man of thirty-nine with hard-set good looks
...where in both cases it's worth noting the hyphen joining the two adjectival terms - which to me implies that the first adjective more closely associates with the immediately-following second adjective than with the actual noun. In my book, an adjective that modifies another adjective is more properly called an adverb (even though it doesn't actually modify a verb, as the name might suggest).
In context, the word set carries very little meaning over and above that conveyed by stiff anyway, but essentially it refers to the physical arrangement, the way the bird is holding its wings. Compare to the setting of a diamond in a wedding ring, or I liked the set of his shoulders (the confident way he held his shoulders; he didn't slouch).