Personally, yes I think I have fully escaped. It's been 16 years since then, and I see my scars as a personal trophy of sorts - a motivator on what I can accomplish if I set my mind to it. It wasn't always like this - but it's what I have conditioned myself to do after the traumas that I have endured related and unrelated to the homelessness.
I hope that you are working to get past any demons that haunt you - you deserve it, everyone does.
I am certainly an outlier and am not sure what the probability of it occurring really is. I think there are systemic issues in how homelessness is treated that I was lucky enough to get past - what concerns me is the lack of support and aide that people in that situation actually receive. Addiction and mental illness barely gets the attention it deserves, and getting people back on their feet is extremely tough regardless of their determination, or skills. I don't want to make it seem easy, because it certainly wasn't - and maybe I did have a one-up in terms of resourcefulness - but without changes in the way homelessness is treated, from government as well as how it can be stigmatized, it's an additional blocker for those trying to re-enter society and make a difference in their lives.
I was homeless for about a year and a half. The first 6 months were spent sleeping on the streets, and when possible, in a shelter - but realistically, in the area where I was, most shelters were not really a safe place to be, and the few that were filled up early. The remaining time, I crashed at a drug dealers house and helped sell in return.
I didn't have much more than the belongings that fit in a mid-sized duffle bag and for a while I mostly survived by cleaning bathrooms at coffee shops before opening hours where the employees didn't really want to do that part of their job - and in return I would get some coffee and a bite to eat. Any money I did get, I saved up.
Once I had access to the internet again, and at least a warm place to sleep at night that I considered safe, I started making contacts on IRC. Eventually I had enough money to relocate across country via Greyhound, a couch to crash on when I arrived and prospects for a new beginning. I quickly jumped from $25k to $40k to $60k etc and am currently at $160k with a whole new life and an amazing career ahead of me.
It's possible to get out of the situation if what got you there isn't addiction or mental illness - the system does little to help, and without being resourceful it's easy to get stuck in that position for a long time. But it can be done. Granted, I never had the ex-con/drug dealer status haunting me in background checks, but I have been upfront in interviews before and still got the job. Greatest accomplishment in life? Escaping homelessness.
I hope that you are working to get past any demons that haunt you - you deserve it, everyone does.