grammaticality - Was "their being followed" replaced by "they're being followed" over the years?

I was reading A Study in Scarlet yesterday and noticed the following sentence:

They must have thought that there was some chance of their being followed, for they would never go out alone, and never after nightfall.

I'm not a native English speaker, when I first saw "their being" I thought it was a typo, and the correct spelling would be "they're [they were] being followed", then I realized the word being was actually the noun, not the verb, that made sense, but I couldn't recall ever seeing this "version" of the expression used. I mostly see "they're being followed", "he's being followed", etc.

With the story being over 200 years old (first published 1887), I assumed this was an old expression that was replaced in later years with the common "they're being", Google Ngram viewer shows a general decrease in use of "their being followed" over the last 300 years, vs a slight increase of "they're being followed" since the 1960's, with the latter form overtaking the former during the mid-1990's.

My question is, is the latter form basically a "mistake" emerging from a typo that was later "accepted"? Or was this caused because th common usage of the word "being" changed from a noun to a verb over the years?