OK...
So, the baseline that we'll use is 2 Corinthians 6:10 because here it is just in a list of of adjectives, and not a specific use, which should indicate how it is treated as a general adjective in Paul's use.
Citing the English of the NIV (btw, I hate the NIV; it's full of errors, but here it suffices for just quick summary of context well enough to everyone here):
sorrowful, yet always rejoicing; poor, yet making many rich; having nothing, and yet possessing everything.
(keep in mind; punctuation does not exist in the Greek, so all of that is interpretation of the translation)
The word for "poor" here is:
πτωχοὶ
It's root is from πτώσσω, meaning "begger"; essentially.
πτωχοὶ would be better represented in English, not as "poor", but "those who are forced into begging", and includes an implication of not only money, but also a loss of social power as well.
In this instance, the conjugation of the adjective is: nominative plural masculine
This conjugation is the conjugation consistent with the grammar of the rest of this citation (all other verbs and adjectives are in the NPM form), except for πολλοὺς, which is APM (accusative plural masculine), which is sensible as it is an adjective of the following direct object (rich, describing how rich the object, rich, are).
So now let's flip to Galatians 2:10:
NIV survey saaays:
All they asked was that we should continue to remember the poor, the very thing I had been eager to do all along.
The word for poor here is:
πτωχῶν
Which is the same word and the same meaning.
The difference here is the conjugation of the adjective, which is genitive plural masculine.
Genitive is ownership.
For example, "the hate of John".
If I meant, "John's hate", then "hate" would be in the genitive.
Otherwise, I would be stating that the hate is a condition held by some group or person regarding John.
Also of note here is the article being used prior to πτωχῶν, "τῶν".
"
The poor" (loosely translating)
This is often used when being specific, for instance; this is how "The Divine" (often rendered in English as "The One God", or something similar) is most often rendered in the Greek.
So it is an adjective that defines a sort of noun, though not grammatically. By inference, it refers to a specific group that is poor, as opposed to the general description of those who are poor.
This is leading the possibility that this may indeed be a specific group that is being discussed, as opposed to a general state of poor people being addressed.
A single comparison is not enough since these are at odds from each other, so we'll look at another entry.
The next best entry for the possibility of a specific poor group is in Acts 24:17.
NIV vomits to us:
“After an absence of several years, I came to Jerusalem to bring my people gifts for the poor and to present offerings.
Oh NIV, you terrible translation you.
"Poor" isn't even in this line in the Greek.
They translate there to be "poor" here from the word they render as "gifts": ἐλεημοσύνας
This is a word for mercy, pity, acts of charity, especially (obviously) when regarding those in need of help.
Here, this word is a noun in the accusative plural feminine.
The feminine is because the gift is received by the direct object.
The direct object here is ἔθνος.
A word for "a people" (essentially); typically implying a racial/national summary.
Here, this word is a noun (obviously) in the accusative singular neuter (neuter because it is all inclusive and not either under or over in grammatical dominance/submission).
As such, (now that I've taken the time to examine it more closely than just reading the English) this entry actually removes my previous question about why bring gifts to the poor here.
There wasn't any poor here being given to.
That concept is being interpreted by the translators based on the possible implication of ἔθνος.
Instead, what it being stated here is that he went to Jerusalem to give offerings to his nation...which would most likely be done at the Temple where he is shown to go and tick someone off for some (as of yet) unknown reason.
So this entry doesn't help too much because it's only a poorly made English translation that inserts the word, "poor", into the line, when it should instead be a line talking about him doing something every Jew "should" do: take offerings to the Temple (at least once in their life; similar to the Islamic practice of Mecca).
So, onward...
The next best entry is Romans 15:26.
NIV, what terrible rendition do you have for us this time?
For Macedonia and Achaia were pleased to make a contribution for the poor among the Lord’s people in Jerusalem.
YAY! Finally a proper entry!
OK, the word here is the same as the first two entries, but follows Galatians pattern:
πτωχοὺς
This is in the accusative plural masculine, which makes sense, since the following phrase is τῶν ἁγίων (the holy...better rendered as sacred or blameless "holy" is an abstract and Hebrew culture didn't think in abstract; everything related to a direct action; in this case, essentially, "those without fault").
Notice that τῶν article?
It exists prior to πτωχοὺς here as well, just like Galatians.
"τοὺς πτωχοὺς τῶν ἁγίων τῶν ἐν Ἰερουσαλήμ. "
loosely, 'those poor of the blameless in the Jerusalem'
So far Galatians and Romans appears to be setting this particular poor up for being a specific group, and not just a general state of poverty; especially Romans, where it is specifically outlined as the 'holy poor' (very loosely translating the concept into English).
So I need at least two more comparisons to be satisfied that I can make a conclusion on this.
Let's see...
2 Corinthians 9:9
NIV, what does your drunk self say?
As it is written:
“They have freely scattered their gifts to the poor;
their righteousness endures forever.”
Nice spacing choice NIV.
OK, well...this is an entirely different word, meaning basically "poor by starvation"...conceptually, and its root means to work or toil just to sustain one's self.
πένησιν is in the dative plural masculine...and is the only use of this word anywhere in the NT.
Oh, good; that's helpful....
Well, this is a crap comparison on the face of it...thanks again NIV for doing a great job at terrible translations.
BTW, this isn't a good representation, because this is more closely related to a state of being hungry for sustenance, and not related to a state of lacking a state of well-doing; which fits the context of the verse.
NEEEEXT!
Acts 10:4 (rogerdodger!)
NIV? You joker you, what do you say?
Cornelius stared at him in fear. “What is it, Lord?” he asked.
The angel answered, “Your prayers and gifts to the poor have come up as a memorial offering before God.
Well, screw it...this one is bad as well.
There's no "poor" here; it's another transnational license NIV took of ἐλεημοσύνας before, but this time it's ἐλεημοσύναι, which is the same word for acts of charity as before...*sigh*.
NEEEEXT!
Acts 9:36
NIV...come on you bastard, give me something I can work with!
In Joppa there was a disciple named Tabitha (in Greek her name is Dorcas); she was always doing good and helping the poor.
Survey saaays?
Good job screwing it up again NIV!
Same as the previous verse...there's no "poor" word here; they are inferring the meaning from the same "mercy/charity/et. al." word used here (ἐλεημοσυνῶν).
And that appears to round up any Pauline citations of "poor".
I can't draw from Luke because I can't just assume that Acts and Luke are actually the same author, so I can't do that.
Conclusions:
Well, it's far less conclusive than I would appreciate (pretty crappy actually), but there's enough possibility between Romans and Galatians compared to 2 Corinthians 6:10 that we can note that there does appear to be a special value placed on the poor listed in Romans and Galatians; clearly in Romans with "holy" being attributed to them, meanwhile the Corinthian citation lacks an article "the/those", and doesn't offer any special note of poor as sacred or holy.
In my opinion, I cannot rule out that Paul is shuffling goods around for a specific poverty sect, and Paul is often found in his letters to claim that giving up all belongings and becoming rich in spirit is his preference (at least...in writing; his actions indicate otherwise).
If this is the case, we don't know if it's specifically
the Ebionites, or another similarly self labeling "poor" group (the Ebionites didn't call themselves, "Ebionites", but instead were referred to as the "poor ones").
This sympathizes with my general stance; that there was a fashion that trended out of the followings of showing that you were poor and calling yourself poor overtly as a rather large portion of the very early believer groups (something that mostly died off over time...because...well...people don't want to be poor; being poor sucks...right Paul? Right.

)
So I would say that the hypothesis can be drafted that Paul is talking about POSSIBLY Ebionites, but they may not be...they may be just another sect of "Poor".
If it weren't for all the focus on "Christ", I'm betting the name for Christianity (had the early followings had their way) would have instead been some derivative of "Impoverished".