“If loan paperwork does not specifically state that a loan company can sell a loan, what legal basis could they have to sell it? “
The lending institution’s name will most likely be stated in the loan documents as “XYZ Bank, it’s Assessors or Assigns” - in which case they can do what they want with the loan.
I am not an attorney, but in the early 1990’s worked in the Commercial Lending Department of two major banks, preparing the loan docs, and it was standard for the instution’s name to say “it’s Assessors or Assigns”.
From dictionary.com , one of the definitions of “assessor” = a person who shares another’s position, rank, or dignity.