Learn English – The passive voice of ”apply”

I think "has been being built" is grammatical, but few people would say it. I think most people would use the impersonal active form you gave.

An alternative in some dialects is "This house has been a-building for years", but that's not in any standard variety as far as I know.

This is an example of Whiz deletion. The sentence is short for:

• There was something which had been placed on the table...

The relative pronoun which and the past perfect form of BE (had been) have been omitted. This is a type of reduced relative clause. For more info on Whiz deletion see this post of John Lawler's on Whiz deletion, and also visit the link therein.

The upshot of this is that your sentence is not a passive 'existential' sentence. It is a case of an 'existential' sentence containing a relative clause. The relative clause is modifying the noun something, and this clause does indeed contain a passive.

Hope this helps!