You are a Hero member here with Activity: 1190, Merit: 754, Posts: 5568. The day you bought this account from that day how many posts you have made, how many merits you have earned and how many activities you have gained? Do you think it was enough for you to be a Hero member if I remove the old data? I guess no, but you are still getting paid for a Hero member in the signature, you are still considered as a Hero member and enjoying the privilege of being a Hero Member.
Interestingly, I've been coming across more accounts that get banned because their previous owner was banned for plagiarism after the sale took place. The most famous case of this happened with bill gator.
But the reason I bring it up is because, as you point out, (unless they specifically make it clear otherwise) they assume
all the characteristics of that account's former identity; for better or worse. Once you take that account you basically become that person. If they didn't have much in the way of a personality, then you have a lot of room to run in developing a new one.
I could theoretically give my account away to a shitposter as a goof, just to see how many posts it could make before somebody spotted that it had changed hands.