In plain English
FAR 52.209-2, Prohibition on Contracting with Inverted Domestic Corporations-Representation, is a solicitation provision prescribed at FAR 9.108-5(a), most recently dated Nov 2015. The complete official text is reproduced below, verbatim, from GSA's published FAR source files.
Its text contains no sentence requiring insertion into subcontracts; see the flowdown section below for what that does and does not mean.
Does it flow down to subcontracts?
No flowdown mandate found in the clause text
This is a solicitation provision — it applies to offerors when submitting an offer, not to contract performance, so subcontract flowdown is generally not the operative question for it.
Where it's prescribed
As prescribed in 9.108-5(a), insert the following provision:
Prescribing reference: FAR 9.108-5(a).
The official text, verbatim
As prescribed in 9.108-5(a), insert the following provision:
Prohibition on Contracting with Inverted Domestic Corporations-Representation (Nov 2015)
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(a) Definitions. "Inverted domestic corporation" and "subsidiary" have the meaning given in the clause of this contract entitled Prohibition on Contracting with Inverted Domestic Corporations (52.209-10).
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(b) Government agencies are not permitted to use appropriated (or otherwise made available) funds for contracts with either an inverted domestic corporation, or a subsidiary of an inverted domestic corporation, unless the exception at 9.108-2(b) applies or the requirement is waived in accordance with the procedures at 9.108-4.
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(c) Representation. The Offeror represents that-
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(1) It □ is, □ is not an inverted domestic corporation; and
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(2) It □ is, □ is not a subsidiary of an inverted domestic corporation.
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(End of provision)