Not to be a pedant, but since Greece to my knowledge doesn't experience ground freezing temperatures, houses there probably do not require (expensive!) ground excavations and basements that take the house's foundation to below the frost line. I have no doubt that in such warm climes a cellar is a very good idea due to the temperature-buffering effect of all that thermal mass around it (useful i.a. for aging cheese and wine and storing other foodstuffs), but to build one would presumably not necessarily be within the financial means of the poor.
Also, once those people start receiving rent from such (or any other) operation, they might no longer be "poor".
Even the place where I live, which must have one of the world's most intellectually-challenged (and by the way also very socialist-oriented, but I repeat myself) governments, basic amenities (water, electricity, etc.) are only provided without charge to the poor for the first X number of units, where X is really very basic survival usage, any usage above that is charged at the usual prices. Not saying that is what the Greeks plan to do, but they would be really stupid to offer "uncapped/limitless".