Cheap housing isn't going to fix this, these people need help to get their life back together, many are suffering from mental health problems but often the support isn't there or the process is too hard for someone on the streets with these issues to pursue, Universal Credit for example really isn't designed for people like this in mind, they will just keep getting sanctioned and then your back on the streets again, it's a never ending cycle.
I just don't believe that the way to motivate people into work is saying you will be homeless and destitute if you fail to follow 'these' guidelines, everyone should have at least a roof over their head and basic amenities regardless of their circumstances, that shouldn't be a luxury afforded by those only with a job or good mental health, give these people the help, support, and stability they need, and then they will have a platform to be able to gain some control in their life and work and improve upon their situation, support in the form of stability is key here, rather than using fear of destitution as a motivator trust that for the whole, human beings want to be happy and successful in life.
Society isn't going to go into meltdown if a very small proportion of people are given free bedsit/apartment and basic allowance/food vouchers to live, we are not all going to give up our jobs and put out feet up and watch sky TV because that assistance is available to us, you have to have trust and have faith in people, in society, we want more than that, I myself have stayed in poor jobs for many years due to being scared to progress because of the real fear of destitution due to a potential failure of a life changing decision, people are scared to make positive change in their life because the safety net isn't there if things go wrong.