I am convinced that he's the Puppet.
The black with white stripes pattern of his shirt matches the Puppet's clothes, & he has a constant stream of tears which is something the Puppet also has.
So there's the visual similarities.
Whoever is saying this is promising to put someone "back together" which is exactly what the Puppet does.

And the Puppet died before any of the others.
Fredbear is still active here, so this has to be pre-Fazbear.
There's no question in my mind. He's the Puppet.

Now, what happened with the child after he died… I'm not really sure. I'd say there are three likely candidates: The Puppet, Golden Freddy, Shadow Freddy

For the Puppet, the evidence is:
- the similar color scheme between the kid's t-shirt and the Puppet.
- the fact that the kid constantly cries in the Mini-games, resembling the Puppet's make up.
- the position the kid takes before fading away, which also closely resembles the Puppet in the "Mangle's Quest" Mini-game.

For Golden Freddy:
- the slouched position, which may symbolize his loss of the frontal lobe, resulting in his inability to behave like the other animatronics.
- the fact that the Fredbear plush followed him pretty much everywhere, and as a result, he took the body of his best friend while alive (not a really good one, I know).

For Shadow Freddy:
- Nightmare. Given that the animatronic only appears after the bite happened, he may be foreshadowing his future after the kid leaves his current body. The game files also seem to imply that Nightmare is the nightmarish version of Shadow Freddy.