We Really Do Care

One character packs their bags and leaves, perhaps because they feel unappreciated, perhaps because they feel they're a burden on their friends, with nothing to contribute. The friends eventually notice and, after a round of mutual recriminations, realize that they're all to blame.

Just as the character is about to board the train, all the friends turn up, telling the character how much they are loved, and begging them to stay.

Sometimes leads to a Ten-Minute Retirement.

Compare You Are Not Alone, The Power of Friendship. Not to be confused with We Care.

Anime & Manga

 * Kirara in Inuyasha, but subverted when it's revealed she was actually called away for an errand by Myoga.
 * Keitaro in Love Hina
 * Komusubi from Eyeshield 21 left the team before the Kyoshin Poseidon game, thinking that his height would be too great of a disadvantage. When this happened, the rest of the team, even including the Hah-hah Brothers and Hiruma, became worried and went to go find him. Though outwardly, Hiruma wasn't so much "worried" as "raging furious that Komusubi would give up so easily".
 * In Fruits Basket, Tohru briefly moves out of Shigure's house when her relatives come back to town, since that's what she'd promised to do. While they all make it clear that they don't want her around, the little Sohma outpost of Shigure, Yuki, and Kyo rediscover the fact that they fail at keeping their household running. In the end, Yuki and Kyo show up when Tohru's relatives are being especially witchy and drag her (not unwillingly) back.
 * One episode of Keroro Gunsou has his mother visit and embarrass her son with her antics. After Keroro snaps and tells her off, she decides to cut her visit short and return home early. Keroro realizes how badly he hurt her feelings and races to catch her at the station....

Comic Books

 * In an issue of Fantastic Four, Sue, feeling increasingly ignored and sidelined by her teammates, is on the verge of quitting the team and becoming a secret agent in Nick Fury's S.H.I.E.L.D organisation. Then she sees a series of TV interviews with her teammates acknowledging that she's the key to their success and that they'd be entirely lost without her, thus convincing her to stay with them. Differs from the trope in that, throughout the issue, the other members of the team aren't even aware that she's intending to leave.

Literature

 * Aahz in Myth-Nomers and Im-Pervections, 8th book in Robert Lynn Asprin's Myth Adventures series. This one does lead to a Ten-Minute Retirement; Aahz is absent from nearly the entire book, while Skeeve has to go as far as Aahz's home dimension of Perv & track him down, in order to ask him to return to M.Y.T.H. Inc.

Live Action TV

 * Joey in Full House.
 * Played (mostly) straight in the final episode of Spaced.
 * River Tam, in Objects in Space, announces that she is turning herself in to a bounty hunter because no one wants her around. Notable in that she never actually intended to leave; it was all part of a Batman Gambit.
 * Subverted in an episode of the Sitcom Roc, where the resident ne'er-do-well announces that he's leaving and storms out. The other characters just make bets on how long he's be gone, ranging from "back in a hour" to "never even gets out of the house". The latter proves to be the winning choice.

Real Life

 * Real Life example: Ringo left The Beatles on an extended holiday after deciding that the band didn't need him. His bandmates weren't long in flying over to ask him back.
 * George Harrison even decorated his drum set with flowers as a welcome-back surprise.
 * Another music industry story: James LaBrie of Dream Theater wrecked his vocal cords after getting severe food poisoning-induced vomiting, which led to a space of about two and a half years to fully recover. During that time he went through bouts of depression and seriously contemplated leaving the band, but the rest of his bandmates convinced him otherwise.