Noun. A Facebook stable is collective group of annoying females who do not necessarily know, nor understand, their boundaries when involving themselves in a friendship with man who is married or in a serious committed relationship. They ignore all indications that the man is in a committed relationship and they "back door" their way into his life, by "liking" his Facebook status often, commenting on his posts, or placing excessive :) or ;) on his wall, along with other subtle messages with uncomfortable innuendo. Facebook stable members disrespect the wife/girlfriend by their facebook actions with the man. Some men choose to keep a "stable" around because it feeds their ego and they relish the attention.
a Facebook Stable member would write, "You're the best, :: insert name :: !:)"
"..thanks for saving ME a bite of that dinner!;) "
and so on.