That is an old ancient record. It was discovered by a student of history at our institute.
Are these two below the same as the combined version of the sentence above? Or do they mean something a bit different?
That is an old ancient record having been discovered by a student of history at our institute.
That is an old ancient record discovered by a student of history at our institute.
So is it impossible for a noun to be modified by 'having been -ed'?
No, it's not impossible in general. It doesn't work with a "There is..." sentence.
The milk, havin been left out on the table overnight, was sour.
The students, having been carted to every historic site the town had to offer, were ready for a break.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
Wouldn't you come up with an example without a comma before 'having been -ed', Barb?
I can't think of a way to use it in a sentence without a comma.
He is very tired, having been up all night working.
The players, having been told that they were sure to win the game, were very surprised when they lost.
Having been spoilt rotten since birth, it was very difficult for him to get used to being poor.
In my opinion, those are examples of reduced adverbial clauses (the first and the third one in particular).