Buck Godot has the Beemahs become this for the Klegdixal, starting in this comic.
Prior to, and unbeknownst to anyone else, the Beemahs were sort of the Morality Pet the Klegs wished they had-the meeting between the Beemah and the Kleg ambassador is kind of a Crowning Moment Of Heartwarming, as the usually rude and self-serving Klegdixal pours his heart out with gratitude to Buck for reuniting the two species, as the Klegs had apparently been the original creators of the Beemahs and their one selfless urge as a species was to fix all the things that had gone wrong in the process (many of them flaws which are used to exploit the Beemahs by another party).
Teeko from Chirault has proved that Kiran is not as much of a stoic loner as he thinks he is.
Collar 6 gives antagonist Mistress Butterfly three personal slaves (somewhere between pet and spouse) who love her and know her to be a good person, though one of them is surprised at her changed personality and calls her on it, getting kicked for his trouble.
Another side of it approaches Morality Chain, as all known Alternate Universe variants of Tedd got a good friend Elliot and at least once the female counterpart Ellen is his girlfriend; the only exclusion is Lord Tedd's world — and instead of Grace there's a big ill-mannered Blood Knight.
Subverted in Furmentation — Alexi goes into a violent, psychopathic rage when his teddy bear is stolen, but having it doesn't seem to make him any nicer than usual.
Built in to troll psychology/romance on a fundamental level in Homestuck. MOIRALLEGIANCE pairs are basically this trope, where a calmer troll keeps a more hot-tempered or violent troll's dangerous tendencies in check and they balance and complement each other's personalities. Three examples exist at the beginning of the troll arc: Kanaya for Vriska, Feferi for Eridan, and Nepeta for Equius. Subverted in that Vriska is still a HUGE BITCH BLUH BLUH even with Kanaya's help, since Kanaya has less-platonic feelings for Vriska and therefore fails to exercise any real control over her, and Feferi broke up with Eridan early on because of the emotional toll of keeping him constantly in check. Nepeta plays it straight except for the fact that on closer examination Equius might not have been that bad a person without her anyways. (He says he might have been.)
The Equius <> Nepeta dynamic is also interesting as Equius believes that he is the one protecting Nepeta; later on, he admits conversely that, without Nepeta's support, he believes he would probably be violently unstable. And since they represent the zodiac, it isn't a very big surprise that Sagittarius and Leo are a dreampair.
Kanaya also finds herself accidentally slipping into this role for Rose, but when Rose mentions it she tries to backpedal because she doesn't want a repeat of her relationship with Vriska.
As of late, Feferi dumping Eridan has had bad consequences for the team. On the flipside, Karkat became one of these for the psychoticGamzee, successfully ending his murder spree without any further bloodshed. Though he stays evil afterwards, acting as a Manipulative Bastard to Terezi and later raising Lord English.
Draconion Dignitary tries to be this to Jack Noir after he's prototyped with Becquerel and becomes crazy but fails since Jack's too far gone. Interestingly played with in that DD isn't a nice guy like this trope usually requires; he's just in favor of Pragmatic Villainy and thinks that Jack is going to ruin everything with his behavior (though there may be some Even Evil Has Standards going on as well). Also subverted with Courtyard Droll who has a lot of traits in common with this trope but is to weak and easily manipulated to be an effective Morality Pet for Jack, and is hated by him anyways.
While technically human, Piffany from Nodwick is the only reason Artax and Yeager actually display any kind of heroism ever. There's a reason A World Without Piffany is so crapsacky it makes even the normal Nodwick world seem pleasant.
Mr. Scruffy the cat is probably the only living thing Belkar genuinely cares for besides himself. While Belkar starts out appreciating what a vicious little bastard the cat can be, this eases him into the foreign idea of having loved ones.
Elan: I can't tell if the cat is a good influence on Belkar, or Belkar is a bad influence on the cat.
Haley: Both, I think, but it probably still averages out somewhere south of Neutral.
Played straight with Blackwing the raven: as the wizard Vaarsuvius' familiar, he gets to mitigate Vaarsuvius' anger issues and remind them of problem-solving strategies that don't involve large explosions.
Played with early in Sluggy Freelance, when Kiki the ferret's regular Catch-Phrase was "Stay good, Riff! Stay good!" Otherwise averted; Torg's Immorality Pet doesn't seem to have changed him, and Bun-Bun's Alternate Reality Good Version didn't stop Torg from sliding into embittered self-interest in the Dimension of Lame.
While he's antisocial rather than villainous, Davan Macintire and his relationship with Rory fit this trope. He's still grouchy and sarcastic around Rory, but he seems to give more of a damn about the kid than he does about most people even upon learning that Rory isn't actually his son.