Actually, the problem is homelessness.

The solution is either housing (ethical) or genocide (unethical).

Provision of housing for the poor can be achieved by means of social housing programs. These can exist in both communist and capitalist societies. E.g. the Netherlands is capitalist, but there is almost no homelessness thanks to its social housing program. The few homeless that are present are choosing this way of life and are therefore not part of problem.