Jorge Aldo's example of Somalia is a very good answer to this part of the question:
Could such a society exist?
Yes. In fact it already does, and has for as long as we've had the idea of society.
However, why he uses Sweden as an icon for human development escapes me. Are long lines, toothpaste tubes filled with caviar, and IKEA giving them high marks in HDI?
As far as this part goes:
What all things should be kept in mind with regards to this?
This simply casts too wide a field. Best answer to this is "Life".
How could this change be brought about?
Number one way this is brought about is war.
It might not be exactly PTSD but massive exposure to violence changes a society. If you didn't grow up in one that experienced it you simply don't know.
Living in a place where you don't believe you have to dedicate a significant amount of your time and money to basic personal security is a privilege. That privilege allows a society to accomplish many great things. Those without it are not "backward". Simply not as privileged.
In the universe that I'm creating, the earth has been destroyed by nuclear wars fought by human kind. Nearly 98% of the population has been wiped out.
The point of the post apocalyptic trope is to remind people that losing a war could happen to you as well. 98% of the population is just a statistic. It would be more dramatic to show that now we have to build our own Apple products.
I was thinking that due to a energy shortage, this group could concentrate power in their hands and as the commoners retaliated, it would gradually lead to an all out nuclear war which wipe out most of the populace.
What again? Sheesh, we never learn.