@Ebithriga
Homelessness in North America has multiple causes. The type you're describing is called chronic homelessness, which is the most "visible" but it's hardly the only type.
For starter, high living costs and weak safety net creates a more transient homelessness that
@MisterXiado describes. Some people get by surfing couches until they rebound, or go back to families. Those unable to rely on such safety nets can end up in a vicious spiral. America is a country that is extraordinarily good at punishing the poor. Everything from overdraft fees to payday lending to the legal system, and of course the medical system, can trip people up. Even the design of cities and the car reliance is a problem. The poorest Japanese has access to public transportation to get to work, or they can just walk. A poor person in the US whose car breaks down and can't go to work can just about get fucked.
Another type of homelessness is youth homelessness. This is an invisible homelessness; teenagers instinctively do *everything* in their power not to "look different," making them difficult to track. Sometimes it's as simple as parents disappearing one day (escaping debt or whatever), others are citizens but their parents aren't, and American immigration authorities don't give a shit if they break a few families along the way, when they deport people. Then there are kids who have been abused and choose to run away from home, or LGBTQ kids who are thrown out by homophobic parents (happens a lot -- LGBTQ kids make up a very significant percentage of youth homelessness).
So, bad shit.
What about Japan? Well, the country has significantly stronger safety net than the USA in parts, similar in parts, and surprisingly much weaker in parts. Youth homelessness can be very similar, especially given how weak Japanese child welfare authorities can be. It's an expensive country, so economic transients also happen -- sometimes uniquely with the phenomenon of permanent manga café clients. And then there are the "tent cities," which are your chronic homeless with mental and/or addiction issues, typically.