(WARNING: Spoilers through the whole movie. Also, it won't make much sense if you haven't seen it)
(Just my explanation to where the white rat in the end came from, and what her connection was to the first Socrates)
She hadn't been in the house when her brother first met him. She got the news when she came to visit, some days later, and their mother had that expression on her nose, the same one of when she started stalking the humans in the library, when she started behaving strangely for her kind. Seemed like it was in the family…
She followed his scent up to the part of the house she never had been to, into the man's room, and then she had found herself staring jaw open. Her brother was peacefully slumbering on the pillow, close to the sleeping man's face, the man's hand next to him like he had fallen asleep cradling the little rat.
She had behaved strangely… but damn, he had burnt the ground!
He opened his eyes at her soft call, and immediately beamed, he ran off the bed and joined her in the wardrobe where the two siblings cuddled and rolled together, happy to see each other again. They both were completely white, and if not for their slightly different smell they looked like perfect copycats to every other rat but their own mother, not to mention the humans.
He had told her about the glue trap, and how the man, at the beginning set on killing him, had then freed him, taken care of him and even given him and the family some food. He had even given him a human name! She knew the sound of it, thanks to her listening to humans, and she explained him that Socrates was a man who lived Long Ago, a very wise one, always questioning and trying to get the best out of people. Socrates, as she was happy to call him now, since he liked it, had been proud of it. He explained his sister that the man was alone, he had no Family, he needed someone to take care of him like of a little one, and Socrates wanted to. Not out of gratitude, obviously. If the man hadn't settled the trap, he wouldn't have needed to be rescued, after all. He just wanted to. His sister wasn't sure she understood, but she nuzzled him, and told him to do what he felt right. He mocked her for talking like their mother, and she immediately tackled, the two rats wrestled playfully for a little till a snort warned them the man was waking up, so she ran away and Socrates went back to him.
She didn't thought anything of this was too weird, she was just happy her brother found someone to care for, and who could feed him, and she went back to her library.
But rats are pessimistic by nature, and even if she liked to behave like the rare ecception her brother really was, in the deep of herself she wasn't too surprised when things suddenly started rotting away fast.
As soon as the man decided to use the other rats for… complicated things, Socrates told their mother and other sister to leave the place, a wise decision. She saw him again only another time. Socrates told her the man needed him more than ever before. He wanted to fix things between the other rats too: Big Ben (that was the name the man gave to the big and bullying rat usually terrifying everybody else) had started behaving like the leader, carrying the rats to raid and own the house in full sunlight, and when rats found themselves following a leader, something they were not prone to, it was always an ugly moment, usually ending bad. He had asked Ben to follow him to the place the man went everyday out of the house, so they could talk. She asked what he planned to do if Ben wanted to fight, he couldn't stand a chance, and Socrates replied Ben was jealous of the man's affection. He wouldn't dare hurt him, for that would mean the man would hate him. What Ben didn't know was the man already hated him, like everybody else in the world but the white rat… Socrates hoped the big rat would never find out. Anyway, that meant he was safe, and he really believed he could persuade Ben to leave and bring the others away... yet, was nervous, he couldn't hide it to his sister. When they parted, he asked her if she would look after his human, in the future. Just in case… things got even more complicated. Complicated as the humans, and the rats who tried behaving like humans, always made them. She promised.
She never saw him again.
She walks and crawls through the conductures of the white and dirty place, trying hard to recognize the trace between all the ugly smells, the chemical ones, and the madness ones. She peeks into so many rooms, listens and sniffs, she avoids the other few rats. They probably won't be interested, but the tale about the man spreaded fast as rats running from a fire, and even if it lasted only some days in the memory of the most, some could still be curious. He was basically dead, and yet he stood up and killed the self-proclaimed leader (of course now nobody said they were actually following Ben's orders…) bare-handed. She doubts of the last part, but at least he hadn't used the bad air, or anything humans usually did, and that gained him enough respect they let him out of there alive. Well, really, no reason why they shouldn't, but following some crazy rat's will: rats don't seek for revenge, and eating humans brings only troubles. So they went away, left him the house… and he had been taken away by other humans. He is alone again.
She stands frozen, at the sudden familiar scent, so feeble she dares not to sniff too hard, then she quickly follows it, running so fast she stumbles on her paws, hits the tube walls with her sides, fast, faster, till she's in the light again, she blinks and looks around, confused, and then she recognizes him. He's laying on the small bed, eyes closed, breath laboured like he's prisoner of a bad dream. She climbs on the blanket and slowly moves close to his face, scarred by bites. She calls softly. His eyes opens suddenly, rageful, and before she can move he has caught her into his hand, squeezing so hard she squeals high in pain… and then he stops. The fingers loosen to a gentle hold, and he looks at her with wide eyes, mouth opening in a silent gasp.
"…Socrates… Socrates, is it you? Oh god… I thought you were… you were… I'm sorry, Socrates, did I hurt you? I'm so sorry…"
He straightens up to a sitting positing, while cradling her into his shaking hands, petting her lovingly.
"You came back to me… Socrates… oh, how I missed you… I'm so sorry for what has happened… but now we're together again… Socrates… my friend… everything will be all right" he is smiling now, a thin, stretched smile broken by sobs, haunted by feverish eyes, but he's smiling. He brings the white rat up to his face and kisses her head, nuzzles her, tears wetting her fur.
Socrates squeals softly, nuzzling back, as to tell the man that yes, everything is all right now.