Hiki-komori is the name. In English it's usually called Social withdrawal syndrome. It got the name in Japanese because a Japanese paediatric described it for the first time. His name however is not commonly known. Had it been an American, say doctor Smith or so, it would probably be called "Smith's syndrome".
But the kids who have it are very miserable.
Just be happy you don't have somethig like that. The manga isn't showing how sad it is, except from the fact that the girl jumps to her death at the end. But in real life, there aren't any loving young men coming to have good sex to a hikikomori that often, let alone those who tell her they will support her for ever. Usually it's a kid who can't even stand to have his parents come into his room and becomes so isolated and lonely he dies or withers away completely, unless he/she gets proper psychiatric therapy.
I don't think the mangaka really knew. He kind of lets it hang in the air. That's one way of ending a story. Called "undisclosed ending".
You don't really know whether the author understands the problem is an actual psychiatric syndrome that's very common; maybe he read in the papers about a girl committing suicide, and that she hadn't been out of her room in ages, and was inspired by that.
Ah! Ashi-girl is a timelapse story, but a very good one. It's about a little teen called Yui, who's not interested in anything (except food, maybe), and has only one talent, that's she can run really fast. As it is in many timelapse stories, she has a genius family member, her little brother, who has buit a time machine. By accident, she gets in there and gets herself zapped into the Sengoku-era: that's the Japanese civil war. Before she's able to realize what has happened, she runs into a fatastically handsome young man, a young feudal lord. And when the lightning strikes her (I mean love at first sight), she doesn't want anything in life anymore but to stay at the side of "Wakagimi" (that means Young Lord in Japanese)... Nobody would guess this lazy teen can deploy such courage and motivation, now that she has a reason in life! This plot is of course just an excuse for the author (Morimoto Kozueko) to paint a historical fresco of that period packed with humour, adventures and romance. It's exciting, incredibly well-drawn, very moving and hysterically funny. It helps if you know a bit about historical Japan; plenty of inuendo about samurai and so... It's full of irresistable side characters, the heroin it totally adorable, and the princely 'Wakagimi' is very worthy of being loved, to say the least...
There, I wrote a review that's worthy of a decent newspaper column.
Anyway, I strongly recommend it, although it isn't translated until the completion. To my great regret. Stupid translators!
Is a syndrome with a Japanese name, since it was a Japanese paediatric psychiatrist who described it, but it exists everywhere. It's a typical form of teenage depression. In Japan they've got specialised therapists for kids with this condition. It can pass, but not always. It's close to agoraphobia and anorexia. Caused by extreme low self-esteem, most common in girls. That's what this story is about.