It is now more or less settled that the author of chapters 1 to 80 of the Dream of the Red Chamber is Cao Xueqin, the grandson of Tsao Yin who was a favourite of Emperor Kang Xi.
It is also accepted now that the last 40 chapters were completed by someone very close to Xueqin, probably a family member.
Hawkes in his excellent Introduction to Vol 1 of his translation said that this interloper was someone familiar with Xueqin ‘s “drafts and wanted a different ending. ” See p 18 Penguin edition 1973.
This statement suggests that Xueqin did complete his novel. However, no such statement or evidence was presented by Hawkes in his Introduction.
The complete 120 chapters were presented in January 1792 in Gao E and Cheng Weiyuan ‘s first printed edition of 1792, referred to by the Chinese literati as the 1791 edition.