I was learning something in Mesechet Brachot about breadcrumbs, and got referred elsewhere to a Gemara in Chulin that reads as follows:
ואמר אביי: מריש הוה אמינא, האי דכנשי נשווראה - משום מנקירותא. אמר לי מר: משום דקשי לעניותא. ההוא גברא, דהוה מהדר עליה שרא דעניותא ולא הוה יכיל ליה - דקא זהיר אנשוורא טובא, יומא חד כרך ליפתא איבלי, אמר: השתא ודאי נפל בידאי, בתר דאכיל - אייתי מרא עקרינהו ליבלי שדינהו לנהרא, שמעיה דקאמר: ווי דאפקיה ההוא גברא מביתיה
Abaye said: At first I thought one collects the breadcrumbs [off the floor] because of cleanliness. My Master said to me: It is because [leaving them on the floor] leads to poverty. There was a certain man whom the Angel of Poverty was following, but he could not prevail over him, because the man was very careful about [collecting] breadcrumbs. One day he ate bread over grass. [The Angel of Poverty said,] "Now he will certainly fall into my hand." After he ate, he took a spade, dug up the grass, and threw it into a river [thus disposing of the breadcrumbs properly]. He then heard [the Angel of Poverty] saying, "Alas, this man has driven [me] out of his house."
Just to give a bit of context here - There are a number of halachot which relate to the idea of not wasting food, and not treating food in a disrespectful manner. This especially regards bread, lechem, considered in Jewish tradition to be the "staff of life" as far as food goes. And just like the English word "bread" is slang for "money", so too lechem is associated with money, livelihood, parnasa. So if you trample on your bread, it's as if you've trampled on your parnasa. If you throw it away, it's like throwing away your livelihood.
The question is, when speaking about handling bread and the effect on one's livelihood, are we talking about something psychological or mystical? In terms of the Angel of Poverty, are we talking about a "spiritual being" or a pedagogical device? And what does that mean in general about how we relate to things supernatural?
As far as what Chazal themselves held, we may never know. Certainly angelology was a part of the belief system of the ancient world, including in Jewish tradition. Chazal talk a great deal about angels of various kinds. So it's definitely reasonable to assume they understood these things literally, that there are supernatural beings appointed over various tasks, and the Angel of Poverty is one of them - albeit one of the "darker" angels, like the Angel of Death and the Prosecuting Angel. Rashi explains the Angel of Poverty as "the ministering angel appointed over poverty, who pursues a person to trap him and bring him to poverty". Now, could it be that Chazal were simply using "angel-talk" because it reflected the language and belief system of the day? Possibly. Though of course when we say "Chazal", we're talking about hundreds of people - certainly not a monolithic group. It could be that some believed in angels while others took the idea with a mythical grain of salt.
But the more pressing question of course is: How do we choose to understand these things?
From my experience, the mainstream frum approach is to believe in angels in the literal sense. There's Gavriel, Michael and Co. who protect us while we sleep. There's the Satan, who tries to trip us up. These are all "real" beings which we could see if only we wore the right spiritually-tinted glasses.
The Angel of Poverty however is a lesser-known entity. When people are concerned about throwing away bread and breadcrumbs, I would guess that most aren't envisioning a supernatural being lurking behind the curtain, ready to zap them with "anti-parnasa" rays if they don't clean up the crumbs. BUT... It seems to me that people do have the sense that if they don't dispose of bread properly, they're leaving open the door for "something bad to happen" concerning their parnasa. It's considered a foolhardy thing to do from a "spiritual mechanics" standpoint. You can try to look up the exact how and why in Kabbalah, but at the end of the day we don't really know how it works... In other words, it's the mystical approach.
The more "rationalist" way of looking at it is either symbolic or psychological. In symbolic terms, breadcrumbs "represent" livelihood. And we show respect for our livelihood by not trampling on that which symbolizes livelihood. In psychological terms, it's saying that by caring for bread, which we associate with money, we will come to show greater care and attention in money matters - and if we're wasteful or careless with the "small stuff", this develops the kind of mindset that will come back to haunt us on a larger scale. Either way, in this way of thinking, there is no "Angel of Poverty". It's a pedagogical, literary device used to convey an idea.
But as I mentioned above, for no other reason than the fact that the Angel of Poverty is a rather "obscure" angel, my sense is that even the traditional frum world is more open to looking at it as non-literal, a literary device - albeit a device used to refer to a "mystical" process.
And here's where I want to push the point a bit.
If the Angel of Poverty can be understood in symbolic/psychological/literary terms, why not the rest of the angelic cavalcade? And if other supernatural beings are rendered in those terms - then why not Hashem Himself?
If it's clear that concept of angels in the Torah tradition arose out of a world where that belief was common, and we're ready to let that go... If we feel comfortable speaking about angels as having a literary and pedagogical function in the text we're looking at, and we focus on the message being conveyed rather than the mythical carrier of that message... Then why can't we do the same with Hashem?
Yes, keep Hashem in the tradition, the same way we keep angels in the tradition. Study the messages from the Hashem-narratives the same way we study angel-stories. But understand that Hashem too arose out of a world where belief in gods was ubiquitous. Understand that it would be absurd in ancient times not to have a deity in one's society and stories. Yes, we have the One deity instead of many. And perhaps Israelite monotheism was a chiddush (novelty), or perhaps not. The "quantity" of gods is not the point. Likewise, the fact that Hashem is the "ultimate superbeing" (and not just one of many "sub-superbeings") is not the point. The point is this: The only reason we're reluctant to take a literary/non-literal view of Hashem like we do with the angels, is that the belief in a law-giving, reward & punishment-doling God has not yet gone out of religious fashion.
But for those who want to be on the "cutting edge" (more accurately called the "just-trying-to-catch-up-with-the-rest-of-the-sensible-modern-world-edge"), there's a place to be a Torah Jew who rejects the supernatural-being concept in its entirety. No, that doesn't mean there isn't more to the universe than we've discovered - just that the Biblical portrayal of God is so obviously not that "more".