How can we encourage kids in social housing to break the chain?

How can we encourage kids who have grown up in social housing to break free of these chains? I'll admit, I don't know the answer to this question.
Can we work together to find a solution?
I want to share with you a story about Cheryl from Rowville, Victoria. Cheryl has given me permission to share her story as she hopes it may prove to be useful food for thought.
Cheryl's story however is really about her son - who is struggling to find his way out of a social housing system which seems hell-intent on keeping him in it.
Cheryl also has two disabled daughters who she cares for full-time as a single mother. Cheryl has been struggling for years to make ends meet (relying on St. Vinnies for food vouchers and dried foods), meanwhile, her son has been focused on gaining employment - whilst living from the family couch. There is simply not enough room for Cheryl, her two disabled daughters and her son.
Cheryl is a victim of domestic violence at the hands of her children's father. The children's father is now out of prison but ensures he pays very little child support by earning a cash-in-hand income only.
Cheryl's son aspires to take his family out of social housing and into private rental accommodation. He wants to take his mother and sisters with him. He has been trying his best to save for the deposit bond and has been preparing to finally break free of the stigma that is being a social welfare recipient.
This was all before public housing bureaucracy automatically adjusted the family income testing to include her son's wages, ever since Cheryl's son gained employment. As a result of this, her son must now pay $200 per week out of his net pay, for Cheryl's rent, in addition to what Cheryl must also pay.
Cheryl's son now feels stripped of ambition and motivation. He feels as though the system is setup to keep him from succeeding. And I can't help but empathise with his situation.
On one hand, we should be ensuring that those on social welfare benefits are means tested to prevent abuse. On the other hand, we shouldn't be stopping people like Cheryl's son from breaking free from social housing.
I think as a society we should be doing everything we can to support each other. That includes supporting the aspirations of people like Cheryl's son. This is vitally important because proactive thinking on the subject will prove to achieve a reduced spend in public housing, which has taken centre stage as a big issue for many Australians and the major political parties.
What do you think?
I hope this story creates a discussion and helps us explore a solution - as I am sure Cheryl's story is not unique and that there are many who aspire to be better than they are, but are being held back by bureaucracy.

Reprinted from here with the author's permission, Anthony Ziebell, and that of Cheryl who is also a friend of impact.