This is something that attracted my attention several times, but I never heard of anyone who wrote about a philosophy of poorness, I guess Marx would be the nearest I've heard of, are there other ones who wrote about it?
I think what you are looking for is a lot older: the ancient greek school of cynicism and maybe even that of the stoics (for they at least preach independence of everything).
To quote from their wiki:
Thus a Cynic has no property and rejects all conventional values of money, fame, power or reputation.
They sought to free themselves from conventions; become self-sufficient; and live only in accordance with nature. They rejected any conventional notions of happiness involving money, power, or fame, to lead entirely virtuous, and thus happy, lives.
It depends on your concept of poorness. Under a certain point of view, I can understand "philosophy of poorness" as the free-willed act of opening hand of your material possessions, except of all those things strictly needed for survival. Thoreau's "Walden" comes to my mind now.
EDIT: For the commenter below :)
I'm still reading it. In general, Thoreau writes about his experience while living for 2 years or so at the borders of the Walden lake, in Concord, Massachusetts, USA, not as a hermit, but as a free man who could attend to his need with the work of his hands only - cultivating his food, building his own house, etc. Whatever money he needed he would get it working as a hourly-paid farm worker on the neighborhood. This money was necessary as he couldn't make everything he needed.
On other book that Thoreau wrote, he stated that he sign a document where he manifested his wishes of "not being considered as part of the people who were attended by the state in his needs, although still being an American citizen", which was accepted and recognized by the local authority.
The later parts of the book are of more philosophical content, which I'm still digesting. After this experience he would conclude that a simpler and more productive life was possible in modern times; that so much were spent and wasted based on pride and vanity that the essential was lost.
So, in whatever this relates to a philosophy of poorness, I guess that's it: the understanding that living in "poorer" conditions may lead to a better experience as living beings.
Jacque Ranciere wrote The Philosopher and his Poor. He mediates on the relationship between the Philosopher which does not belong to the Poor and the Poor themselves; and the fascination that the Poor have exerted on his thought from Antiquity to the present day; of course this is as true for Western Philosophy as well as Philosophy done elsewhere - say Buddhistic or Islamic.
It seems like a good place to start but I can't comment critically as I haven't read the book myself.
I do think that one should make a distinction between the Poor and the Ascetic which more about the cultivation of other virtues rather than riches - buddhists, stoics, cynics etc.
The Poor that you mention seems to be more akin to the proletariat of Marx.
Your question raises some interesting issues about philosophy itself. It may be that "poverty" is not an issue that can be framed philosophically, at least not in the traditional sense.
Marx was certainly trained philosophically and was one of the great thinkers of his age. But were his major works philosophy per se? In "Thesis on Feurerbach" Marx famously rejects the "armchair" philosophy of those who merely describe the world, rather than seeking to change it.
"Das Kapital" and his other mature works engaged primarily with the British political-economists and French socialists, adopting the methods but not the issues of German idealism. He did not explicitly concern himself with ontology or epistemology, and appeared to accept an almost naive naturalism. Given his task and intent he really could not do otherwise. He was thus arguably one of the first post-philosophers who might be better described as a critical theorist, economist, or sociologist.
The point is this. Philosophy tends to seed and shed disciplines. Theology, psychology, and physics, notably. Thus, Newton, Adam Smith, Marx, Freud, Weber, Einstein, Adorno, Kuhn, and so on, pursue their aims in ways that are no longer readily departmentalized as "philosophy." Why not? While philosophy can deal with any issue, it tends to universalize. It adopts a general stance with respect to metaphysical questions that transcend specific cultures, times, and places. And many, including Marx and Ranciere, have criticized it for precisely this recumbent detachment.
While "poverty" might appear universal, as a subject of theology, for example, the structure, meaning, and analysis of poverty is really relative to particular social conditions. Marx and Engels illustrate this most brilliantly in their emphasis on history, "praxis," and analysis of modernity, explicitly "standing Hegel on his feet." (I believe Marx said "head" but should have said "feet.") Many subsequent Marxists, from Lenin to the Frankfurt School, may know their Aristotle, Kant, and Hegel, but take the label "philosophical" almost as an insult, an accusation of pipe-puffing disengagement.
Most serious engagements with "poverty" implicitly treat it as a problem to be analyzed and solved, which ontology, epistemology, and even, to some extent, morals in the universal or theological sense, are not equipped to do. The issue is thus claimed by some of the more defined subfields seeded by philosophy: political theory, legal theory, sociology, economics, theology. The analytical tradition, in particular, explicitly avoided "value" issues, and addressing social concerns like poverty was only lately returned to analytical respectability by Rawls, Singer, Sen, and others.
There are no fixed boundaries. But in certain historical respects, philosophy proper is an unapologetically "armchair" pursuit. It can do its work without data, news, or experiment. When it finally rouses itself to the laboratory, law courts, or barricades, it no longer calls itself philosophy.
" I guess Marx would be the nearest " .. He wrote pretty extensively on this very thing. you cannot ( i believe ) write on the philosophy of "poorness" without mentioning its antithesis "rich" . Das Kapital being the convergence of the ideas of capitalism between the two groups. Poverty can only be measured based on its difference to wealth or "richness" . Although you are not specific in this question of your meaning or relationship to "poor" I am only guessing that it is of economical in nature , by the mere fact that you mentioned Marx.
Unless you mean "poor" in every sense, which would lead to regression and i guess the study of negativity.
Economically though Marx outlines in Das Kapital "contradictory character of the economic value of the commodity (cell-unit) of a capitalist society" which is basically about a recession and inevitable actions of those who are poor and the use of mass poverty by the bourgeoisie into order to create the illusion of greater power and the decreasing of wages to create larger wealth as the top dogs fight for position.
This is very apparent in today's society where the writing's of Marx are very real. Where bankers who make millions of dollars every year even in years where their very actions cause the destruction of countries, still get million dollar bonus and multi billion dollar payouts , all on the backs of the poor. Its basically monetary disparate, aided by the governments in the knowledge of the mental disparity of the masses during such radical economic transitions.
In democracy, outlined by the Greeks and the founding fathers of America and to a degree Plato's republic, the majority tends to be lead by a small minority in decisions of the communities and countries for the benefit of everyone
"Democracy is a form of government in which all eligible citizens have an equal say in the decisions that affect their lives"
Yet today in this so called free democracy that American seems to have to export to every country for fear of complete world instability by communism and the infringement of the basic human rights of freedom ( god forbid you tell them about the hypocrisy of Guantanamo bay and the inherent flaw of rationality, in freeing countries with war ) we have less power then ever before. By the people, for the people is not so anymore. And government's the world over have inherited this insestual illusion of democracy where politicians are backed by multi-trillion dollar multi nationals , making decisions based on the good of those organizations no matter the cost to the environment or the greater population, who inevitably become ( like in the matrix ) a battery to further power the machine that is capitalism. Feeding the 1% that walk this world like giants at the expense and destruction of human life and morality. This is basically existentialism gone completely retarded and the ramifications as such are the billions of humans struggling each day just to make ends meet. Played on like puppets by the price of oil.
Not for one second do they seem to see the amazing creative potential of the whole of societies working together through their differences to create and produce in accordance with the laws of nature. Capitalism might not be our destruction but it will be the driving force to a pool of lost potential and the stagnation of the whole, with regards to humanity.
Philosophy tending towards ethics could also be taken with regard to "poorness", with the likes of Peter Singer ,John Rawls and Nigel Dower.