If I was in command of the defenders, I'd have my most observant and sharp eyed soldiers observe the besiegers, watching for any attention lulls, patrols, lightly/weakly/un-defended areas of the surrounding area. When the opportunity was right, I'd send 20 of my best men out to sneak past the lines, taking our squads of soldiers through ambush, and picking off patrols before they realize what happens. There are normally sally ports that are a bit hidden from view and hard to find used for sneaking men/supplies in and out.