Why has being been used instead of is? Will it be wrong if I use is?
Because this is an absolute clause. It modifies the main clause - the part of the sentence before the comma.
If you used is, it would become a stand-alone, independent clause. You would need either to use a semicolon to divide the two clauses, or just break the sentence outright into two separate sentences:
Originally the pile of plush consisted of mohair or worsted yarn, but now silk by itself or with a cotton backing is used for plush. The distinction from velvet is found in the longer and less dense pile of plush.
Thus, it will be wrong only if you change the ing form into the finite-verb form is and make no further changes.
Here's a simple example of an absolute construction:
CopperKettle's answer read, Nazmul scrunched up his brow, trying hard to understand what absolute clause meant.
See: "CopperKettle's answer read" is not explicitly bound to the main clause, but it is logically connected to it - to the whole of it, not to some particular word.
An absolute clause can use a non-finite verb (an ing or ed verb - like "being" or "read"), but not a finite verb like is.
You could break down this example sentence into two sentences if you want to get rid of the absolute clause:
CopperKettle's answer was read. Nazmul scrunched up his brow, trying hard to understand what absolute clause meant. (the verb was is a finite verb)
Quirk et al., A Comprehensive Grammar of the English Language, Unit 15.58, "Nonfinite and verbless adverbial clauses".
P.S. Concerning your comment question,
Is "trying hard to understand what absolute clause meant" also a absolute clause?
No, it's a non-finite adverbial clause. It modifies the verb phrase "scrunched up his brow". And the "understood subject" of this clause is Nazmul: it is identical in reference to the subject of the superordinate clause.
How to distinguish an absolute clause? It usually contains a noun to which the non-finite verb connects. This noun (or noun phrase) is an "overt subject" of the clause. Take, for example, such formulaic absolute constructions as "God willing" (noun: God), "Weather permitting" (noun: weather).
Example of a sentence where one non-finite clause is an adverbial, the other is an absolute construction:
At night returning, every labor sped,
He sits him down the monarch of a shed:
Smiles by his cheerful fire, and round surveys,
His children’s looks, that brighten at the blaze;
The absolute clause is "every labor sped". The past participle "sped" describes the noun "labor". "Every labor was sped".
The adverbial non-finite clause is "at night returning" - it contains no logical subject for "returning", and is connected to the verb phrase "sits him down the monarch of a shed". Its 'understood subject' is "He".