This is a fascinating and complex story.
Ben Sira (Jesus son of Sirach) originally wrote in Hebrew. His book was turned into Greek by his grandson. That's the form of Greek text found in the major uncials (Vaticanus, Sinaiticus, and Alexandrinus), and is often nowadays called GI. But various additions were made by later hands, perhaps mainly during the last century before Christ, resulting in interesting expanded Greek texts--often called GII.
The KJV translators had access to three published Septuagints: the Complutensian, Aldine, and Sixtine editions. They used all three, but when translating Jesus son of Sirach they relied mainly on the Complutensian Polyglot, which was based on the GII manuscript 248. That's why the KJV has an expanded text of this book.
Most modern Septuagints are based mainly on the great uncials and therefore contain a shorter (GI) text. However, recently there's been a revival of interest in the GII form. Rahlfs, in his 1935 Septuagint, printed only GI in the text and left the GII additions in the textual appartus, but Ziegler's more recent edition of the book in the big Göttingen Septuagint series prints all the GII additions in the text itself (in a smaller font than the GI material). The same policy has been adopted by NETS.
The KJV translators had no access to the original Hebrew (parts of which began to be rediscovered only in 1896).