Problem: Homelessness exists. Untrained workers might be worth too little to hire, and they cannot receive training. This is how the cycle of joblessness starts.
Solution: Break the cycle by allowing workers to take jobs even when they pay less than minimum wage; and give them a tax break until they gain financial momentum. Specifically: eliminate the minimum wage and increase the standard tax deduction to $25k.
Implications: A huge new number of low-paying jobs would open up, offering an opportunity for training and experience to young or untrained workers. And everyone earning $25k/year or less would have no tax bill at the end of the year. The large number of new workers and jobs would rapidly grow the economy. This might not completely eliminate homelessness, but it would help a great deal. Far more jobs would be created than would be filled, so those earning the minimum wage now should expect that the job market would become more attractive, and offer better income to those with some experience or training.