I bet everyone saw this long post coming a mile away ;p
Why did Curly sacrifice herself... Well...
In my opinion Curly Brace is somewhat of a broken robot.
You pretty much covered it, "...abandoning one's only source of air and letting oneself to drown doesn't look like self-preservation to me. ... The more logical thing would be to leave Quote in the Core Chamber (or what's it called). Who the hell is he, anyway? ... What would you do? Save a total stranger and die? ... Oh! A tow rope! Maybe I should bring him with me, he could be useful later on..."
Curly Brace...
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Facts :
1) You meet Curly as soon as you enter the sand zone, and she recognizes you as a scout robot immediately. She however does not engage and fight you immediately. And instead returns to the Mimigas she is protecting...
Doesn't that seem illogical? If she is protecting her Mimigas shouldn't she face you before letting you have a chance to kill her Korons?
Maybe she doesn't have her machine gun with her? Perhaps...
Maybe she is rushing back to make sure nobody has slipped past her and to make sure they are okay? Perhaps...
Or maybe... there's something between Quote and Curly. No, there is no accessible memory of that something. But, there's something there. She sees you and instead of confronting you immediately or before you make it to the Mimigas she looks at you for a long second before getting out of there.
And also I might ask what was she doing there? It seems odd that she would have just been standing there. I mean maybe she was collecting food, or had been using the teleporters... But, I still think there's something about Curly's behavior. She may have lost her memory, but we know it still existed within her somehow, as the mushroom magically restores it... (somehow..strangely hmm... hmm....)
2) When you confront her she doesn't give you a chance to explain and you basically have to fight life or death to take her out before she takes you out. A bit brash?
Maybe it took her a while to process why she recognized you? Ah! You must be one of those killer robots!
Well in any case you can see she takes things to the extreme when she finally does something.
3) After defeating her and telling her you are with the Mimigas. She just completely flips her story, and is
that's right! That might mean she is very trusting when she gives you a chance to say or do something...
4) She had high hopes for you
But she ended up bady damaged in a battle against Misery. [the battle must have been with Misery because, Balrog was sent to the Labyrinth. And it couldn't have happened on the way to the warehouse because Curly tells you she had high hopes for you, and hoped you could have taken out Misery/Balrog... Wait how did she even know they were around? Well maybe she talked with Jenka... ... wait maybe I'm wrong even yet. Well, when Curly got attacked by Misery, I imagine when she got defeated by Misery she exclaimed that a certain Robot will make you pay...]
But there you are, and she loses hope; she quickly sinks into despair, since she can't do anything, can't even move.
She's quick to accept the situation. But also brash and optimistic and trusting.
5) Quote saves Curly. You give the doctor the Cure-All restoring Curly, essentially saving her. She immediately goes after you [somehow passing you, probably more ways to get there in a 3d world, probably a safer way than Monster X's battle.]
She's eager to help you when you meet with her.
6) Balrog shows up and Curly is oblivious to the danger, and simply shouts, get in the middle! Help us! This is completely illogical and as you see, Curly was completely open to attack and gets plastered by Balrog when she leaves herself completely open...
Another demonstration of how she is somewhat oblivious and trusting.
7) Even after getting knocked out by Balrog she immediately forgives him when he helps out...
'He doesn't seem like a bad guy actually..!'
Then she's ready to kick ass and chew bubblegum in the monster's nest...
You know... she could be drawn to Quote for a reason beyond her understanding. Or perhaps she has some programming in her that sends her closer and closer to the core. Or it could just be coincidence as that's the only way out.
A person like Misery or the Doctor would probably call her simple minded. "That's what I hate about robots..."
8) Finally at the Core Base, she shows little caution and presses onwards with no hesitation. She has a lot of information though. Reflect on how quickly she recognizes Quote, his Polar Star, the place as a Base, how to fight, etc... But on the flip side, she rushes into things with little caution.
She doesn't wait for Quote before proceeding, as Quote does all the button pushing to open the doors. And when she notices for some reason the 4th gate is jammed, she simply looks at it...
But don't think her lazy or stupid. There's another possibility. All of these things she has been seeing, could be triggering lost memories or tugging at them. This is random, but there is probably significance to the jamming of the 4th gate.
Think of it like deja vu or a dream. You see something that you think you've seen before. Yet you can't place it anywhere. This is the kind of theory I have for Curly...
9) Yes this is it at last... After Curly and Misery trade words, we see that Curly had no clue about what the Core was. She fought against it because it was trying to kill them is basically it.
Soon as Misery leaves the water begins to rise, and Curly stops moving. She doesn't run around trying to find a way out, doesn't shout to Quote or even respond to Quote if you try to talk to her. She doesn't even look around she has her back turned.
Now I don't think she's just lazy or stupid and is thinking, "well now I take a nap". I sincerely think something is happening inside of her. In my opinion she is finally starting to remember something about her past.
Seems too random? Well, have you seen this post ? :
http://www.cavestory.org/forums/posts/40761/
It talks about another theory relating to the whole Ballos storyline that seems to come out of nowhere... In my opinion Curly might be having something similar happen to her. Maybe those same words? "Did you know that the witch-woman... etc" or whatever, in any case maybe that is making her remember something...
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Quote is drowning before her, already at the point of freezing up.
Now you have some theories to work with :
She saves Quote because she's brash. Logic dictates that if Quote can defeat Curly, Quote should be the one to save them. He has the better odds.
She saves Quote because she is quick in intelligence, but not common sense. Perhaps Curly Brace realizes Quote won't last as long as Curly underwater.
She saves Quote because she is brash and often does things that are illogical. Quote spared her when they fought. Quote saved her when she was injured. This choice might be the most natural in the world to her.
She saves Quote because something is triggering inside her. Maybe it's a program. The same reason why Quote and Curly are compelled to reach Hell, and have those narration flashbacks. Maybe she realizes Quote is invaluable. He has to take priority...
She saves Quote because something is triggering inside her. Her memory. Perhaps it's only some images, or a feeling or abstract and incomplete data. Maybe being with Quote is the most natural thing in the world, and/or she experienced a similar situation once. If she remembered Quote somehow, then it might completely affect the choice she makes to believe in Quote.
Foolish? Trusting? Illogical? Not concerned for her own well-being compared to others?
This is why I call her a broken robot. But it's also why I love her lol
I have this picture in my mind, that the first time Quote and Curly meets, it's because she foolishly protects Quote against overwhelming odds.
Picture it : Quote the one man army, is placed in a terrible situation. Ambush? He takes out countless enemies, but simply can't stop all of them. In the blazing scene there are just too many. Knocked down, it seems like death is finally here and he accepts it. But then, a robot never created for war holding a fallen enemy's weapon, stands in front of Quote alone protecting him.
This is the kind of flawed personality I think she has...