I first encountered Fugly back in early May 2015. Totally by accident.

I was doing my thing in the Blue Line Station when I noticed faint footsteps approaching my position. Looking across to the other side of the floor I was on, a smallish figure was very slowly approaching.
A mutant.
I immediately readied my weapon, but quickly realised that it seemed calm and not alerted by my presence at all. In fact, it acted as if I was an ally, totally oblivious to my true identity. It stopped in front of me, gave me a vacant look and started talking in that mumbling, gurgling way the mutants do. It was all very amusing. Obviously a glitch, because I've played the game a few times by then but that had never happened before.
It followed me around wherever I went, even down the stairs as far back as the start of the level. Some things I did and some areas I led the mutant to triggered his hostile side and resulted in me having to kill it, but avoiding those parts of the level I had a strange sidekick accompanying me, babbling away in its strange speech.
At the time I didn't have game recording capability and could only take some screenshots. I told my good Australian friend Redback about the incident, who came up with the name 'Fugly', because, let's face it, the little guy is ... freakingly ugly. The name stuck.

Redback, who was able to replicate the glitch, made a video recording of Fugly around that time and posted it. I here present my own video recording for the first time below.

Screenshots:

Mission: Mutant Expansion (for Mayor Redstone and Foreman Jones in Subway Town)
Location: Blue Line Station (first visit)

Remember to save before entering the area so you can reload a save in case you don't trigger the glitch.

To replicate the scenario in which Fugly appears, I follow a particular but simple procedure.

Once inside the area shown at the start of the video,
1) head up the stairs, turn right and watch as a mutant flees into a hole behind a shop screen. Don't go to the left side (yet), as this seems to prevent the glitch from happening.
2) Equip the shotgun with pulse ammo. Open the screen by shooting the control panel. Go inside, walk around in there a bit and listen for faint footsteps coming your way, indicating that the glitch has been triggered. He'll be approaching slowly from the restrooms on the opposite side of the floor you're on.

IMPORTANT: Things that (can) cancel the glitch:
• Shooting at any of the mutants before you meet Fugly. This seems to be vital in triggering the glitch. Don't shoot at or kill any of them from the moment you enter the station to when you open the shop screen. There is no need anyway. They all scatter when you approach and none will attack you.
• Of course, shooting at Fugly will make him hostile.
• Getting too close or bumping into him. (He may start to swing his club without moving from the spot.)
• Taking the money from the vending machines that are closest to the restroom, or picking up the tools (wrenches) from the floor there. He tends to disappear into a wall when you do that.
• Going into the restroom area where he came from.
• Picking up the TNT in the area close to the restroom.

As soon as you retrieve the explosives (TNT) - the first mission objective - mutants will start attacking. Once you start to defend yourself, Fugly will awake from his friendly state as if suddenly realising who you really are and join his brethren in the attack. Then you have no option but to take him out.

Now, whenever I replay RAGE, I make sure to trigger Fugly just for the fun of it. For a short few minutes I can call myself 'mutant friend' and listen to him making small talk. Hey, I think I'm picking up a few words even. :)

Twin Fuglies
On rare occasions I was able to trigger not one but two "friendly" mutants using the same procedure. I don't know what causes this; maybe a glitch within a glitch? See if you can replicate it.

Screenshots:

Duration: 5:51