Although I highly doubt you're sincere in this post, defining the parameters of homelessness is indeed a necessary first step.
With that being said, many have worked at defining it much more in depth than (probably) anyone on on here.
The definition only goes so far. There's also a variety of types of homelessness (from a quick search on the internet):
Situational or transitional/short-term homelessness is defined as a person forced into homelessness due to a life event (loss of a job, disaster, losing a family member who is the breadwinner, domestic violence).
Episodic or cyclical homelessness occurs when a person falls in and out of being homeless, many times due to mental illness or addiction.
Chronic/long term homelessness is the term used for a person who is homeless for long periods of time usually because they don’t have the resources (family, friends, etc.) to change their living situation. These too are often people experiencing ongoing mental health or addiction issues.
http://www.bincfoundation.org/what-is-homelessness/But these definitions and categories only scratch the surface.
The question is what to do about it, right?
One thing that could be done right off the bat is creating more affordable housing. If someone loses their home due to a job loss, natural disaster, illness or whatever - and have no family to take them in, the only thing they'd have to turn to is public housing. And, sadly, most choose the streets over that because they're either overcrowded, in a terrible part of town or just not available in time.
I've seen this firsthand in Chicago. People choose to live on the street over going to shelters because of overcrowding and the terrible conditions in many of them. Those that are well maintained are full 99% of the time.
We desperately need more affordable housing in this city - and all over the country. Giving lip service serves no one. Actually building the buildings needs to happen.
Obviously buildings are only one part of a much larger puzzle. Along with these buildings, you'd need to have better means testing. You'd have to control rents. You'd have to protect the tenants as well as the landlords.
Like it or not, this is a government issue and would have to be handled by them. Affordable/public housing.
Not an easy task - but nothing worthwhile ever is. (old cliche, but true)