And the saddest part is that most do not want to get out of that situation.
For several years I was associated with a non-profit Veteran shelter. This was not run by the VA, but a private organization. And they would take just about any Veteran that came to them, so long as they were drug and alcohol free for at least 30 days.
And the 2 biggest problems they had was keeping out those that were not Vets, and of getting Vets who were clean the mandatory time and would stay clean. I think the fail rate for their 6 month program was about 60%, primarily because of drugs. But of course, the largest problem was actually getting real Vets in the first place.
I was living there and helping out at various "Homeless Vet Stand-Downs", and I saw the problem first hand. Most of those events are during 3 day weekends, like Veterans and Memorial Days.
First day, we would have tents and showers and medical care and the like set up for the "Homeless Vets". We would clean them up, give them new clothes, and get them help with either us or the VA. And we would be swamped, literally 400-500 people filling the "Tent City", and the VA would be scrambling to get confirmation of military service for these individuals.
By day 2, we might have 200-300 people, almost all of the others asked to leave when the VA could not verify any kind of military service.
On Day 3, literally only a few were left. On average, 75-80% were shown to have no military service at all. And the rest normally had dependence issues, and did not want help getting cleaned up at all, they just wanted some free stuff.
But we normally helped 100 or so real veterans to some degree, generally arranging some kind of program for around 10-15% of those.
I was lucky, in that I never lost hope. My homelessness was economic, not because of drugs or alcohol or mental illness. In LA, if you are out of work for more then 2 months you are in serious danger of loosing your home, because unemployment does not even pay the rent, let alone all your other expenses. So I would cycle between loosing my home, working to get back into a place again, then loosing it again when I had to look for work. That was my main motivation for leaving that area, I could not stand living in that kind of cycle anymore.