يَٰٓأَيُّهَا ٱلنَّاسُ أَنتُمُ ٱلْفُقَرَآءُ إِلَى ٱللَّهِ وَٱللَّهُ هُوَ ٱلْغَنِىُّ ٱلْحَمِيدُ
"O people! It is you who are in need of God. God is the One who needs nothing and is worthy of all praise."
The lexicographers give the concrete sense of the root thus: faqar, the spine; faqīr, the one whose spine is broken. From this arises the sense of neediness: one who cannot stand up on his own.
I record this picture and transmit it as a connection the lexicographers make, not as a settled verdict of etymology.
And the way the sentence is built is worth recording: antumu'l-fuqarāʾu ila'llāh — the predicate comes definite. In Arabic this conveys restriction (ḥaṣr): "the truly needy ones are you."
And the other side is mentioned by two names: al-ghaniyy (the one who needs nothing) and al-ḥamīd (the one worthy of praise). The addition of the second is worth recording: to be without need might on its own have conveyed a distance; the attribute of praise keeps the relationship open.