Another perspective based on some sources mentioned in other answers, but not yet elaborated upon:
There is an obligation to fill the needs of a poor person that are lacking.
This applies even if the poor person was used to riding on a horse with a servant running in front of him, and he lost that, then people are obligated to fill what he lacked.
Source: Rambam, Hilchos Matanos Aniyim, Chapter 7, halacha 3 [and Gemara etc.]:
"3 We are commanded to give a poor person according to what he lacks.
If he lacks clothes, we should clothe him. If he lacks household
utensils, we should purchase them for him. If he is unmarried, we
should help him marry. And for an unmarried woman, we should find a
husband for her.
Even if the personal habit of this poor person was to ride on a horse
and to have a servant run before him7 and then he became impoverished
and lost his wealth, we should buy a horse for him to ride and a
servant to run before him.8 [This is implied by Deuteronomy 15:8
which] speaks [of providing him with] "enough to [fill the] lack that
he feels."9 You are commanded to fill his lack, but you are not
obligated to enrich him.10
ג לְפִי מַה שֶּׁחָסֵר הֶעָנִי אַתָּה מְצֻוֶּה לִתֵּן לוֹ. אִם אֵין לוֹ
כְּסוּת מְכַסִּים אוֹתוֹ. אִם אֵין לוֹ כְּלֵי בַּיִת קוֹנִין לוֹ. אִם
אֵין לוֹ אִשָּׁה מַשִּׂיאִין אוֹתוֹ. וְאִם הָיְתָה אִשָּׁה מַשִּׂיאִין
אוֹתָהּ לְאִישׁ. אֲפִלּוּ הָיָה דַּרְכּוֹ שֶׁל זֶה הֶעָנִי לִרְכֹּב
עַל הַסּוּס וְעֶבֶד רָץ לְפָנָיו וְהֶעֱנִי וְיָרַד מִנְּכָסָיו קוֹנִין
לוֹ סוּס לִרְכֹּב עָלָיו וְעֶבֶד לָרוּץ לְפָנָיו שֶׁנֶּאֱמַר (דברים טו
ח) "דֵּי מַחְסֹרוֹ אֲשֶׁר יֶחְסַר לוֹ". וּמְצֻוֶּה אַתָּה לְהַשְׁלִים
חֶסְרוֹנוֹ וְאֵין אַתָּה מְצֻוֶּה לְעַשְּׁרוֹ:"
But what if the poor person asks to fill what he was lacking, and the person he's asking doesn't have enough to give him?
[see Halacha 5 there]:
When a poor person comes and asks for his needs to be met and the giver does not have the financial capacity, he should give him according to his financial capacity.
How much? The most desirable way of performing the mitzvah is to give one fifth of one's financial resources.12 Giving one tenth is an ordinary measure.13 Giving less [than that] reflects parsimony. A person should never refrain from giving less than a third of a shekel a year.14 A person who gives less than this has not fulfilled the mitzvah. Even a poor person who derives his livelihood from charity is obligated to give charity to another person.
בָּא הֶעָנִי וְשָׁאַל דֵּי מַחֲסוֹרוֹ וְאֵין יַד הַנּוֹתֵן מַשֶּׂגֶת נוֹתֵן לוֹ כְּפִי הַשָּׂגַת יָדוֹ וְכַמָּה עַד חֲמִישִׁית נְכָסָיו מִצְוָה מִן הַמֻּבְחָר. וְאֶחָד מֵעֲשָׂרָה בִּנְכָסָיו בֵּינוֹנִי. פָּחוֹת מִכָּאן עַיִן רָעָה. וּלְעוֹלָם לֹא יִמְנַע עַצְמוֹ מִשְּׁלִישִׁית הַשֶּׁקֶל בְּשָׁנָה. וְכָל הַנּוֹתֵן פָּחוֹת מִזֶּה לֹא קִיֵּם מִצְוָה. וַאֲפִלּוּ עָנִי הַמִּתְפַּרְנֵס מִן הַצְּדָקָה חַיָּב לִתֵּן צְדָקָה לְאַחֵר:"
and the note  elaborates upon the obligation for a "5th" on chabad.org, that it shouldn't be more than a 5ht:
This also reflects an upper limit. As Ketubot 50a states: "Even a person who distributes money to charity with largess should not distribute more than a fifth." This concept is derived from Jacob's vow to tithe (Genesis 28:22). There the verb which conveys the promise to tithe is repeated, allowing for the concept of giving two tithes. See also Hilchot Arachin 8:13 which cites Leviticus 27:28 which speaks of a person designating a dedication offering "from all that is his." The Rambam continues:
[Implied is that he should not give] "all that is his," as our Sages explained. This is not piety, but foolishness, for he will lose all his money and become dependent on others. We should not show mercy to such a person. In a similar vein, our Sages said: "A man of foolish piety is among those who destroy the world." Instead, a person who distributes his money for mitzvot should not distribute more than a fifth, and he should conduct himself as our Prophets advised [cf. Psalms 112:5]: "He arranges his affairs with judgment," both with regard to matters involving Torah and worldly concerns.
Yayin Malchut notes that in his Commentary to the Mishnah (Pe'ah 1:1), the Rambam writes that as an act of piety, a person may give more than a fifth. Nevertheless, there is not necessarily a contradiction between the two. In his Commentary to the Mishnah, the Rambam is speaking about giving to a needy person who asks for alms. In response to that acute need, one may give more that a fifth. Here the Rambam is speaking about giving to charity when there is no acute need. Hence a limit can be established. See also Ketubot 67b which states that these restrictions apply during a person's lifetime. He may leave a greater percentage of his resources to charity in his will.
In Iggeret HaTeshuvah, Rav Shneur Zalman of Liadi states that one may give more than a fifth of his resources to charity to atone for his sins, for just as one is not concerned with the amount one gives when it comes to healing a physical wound or blemish, so too, one should not be worried about cost when healing a spiritual blemish."
The question is if this applies to one fifth of the giver's total resources at the time the poor person asks, or one fifth of what that person makes going forward etc., and what if he already gave one fifth from the income he made before, can he give one fifth of the total if the poor man asks again?