As stated in the title.
Webbed melee enemies attack when you get close to them. Archers don't, at least not the neutral ones...
I tested it with Wildling and Bandid Archers - if you web them(used black widow), they stop shooting until the web ends. Maybe because they usually would move first, then shoot - since they can't do the first thing, they stop alltogether. If you get into melee range with them, they don't shoot either.