In plain English
FAR 52.216-11, Cost Contract-No Fee, is a contract clause prescribed at FAR 16.307(e), most recently dated Apr 1984. 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
We scanned the full clause text and found no sentence directing the contractor to insert this clause into subcontracts. That is a statement about the text, not legal advice: a prime contractor may still flow terms down contractually, an agency supplement (DFARS, VAAR, …) may add requirements, and clauses listed below (if any) may order this clause into subcontracts from the outside.
Where it's prescribed
As prescribed in 16.307(e), insert the clause in solicitations and contracts when a cost-reimbursement contract is contemplated that provides no fee and is not a cost-sharing contract. This clause may be modified by substituting "$10,000" in lieu of "$100,000" as the maximum reserve in paragraph (b) if the Contractor is a nonprofit organization.
Prescribing reference: FAR 16.307(e).
The official text, verbatim
As prescribed in 16.307(e), insert the clause in solicitations and contracts when a cost-reimbursement contract is contemplated that provides no fee and is not a cost-sharing contract. This clause may be modified by substituting "$10,000" in lieu of "$100,000" as the maximum reserve in paragraph (b) if the Contractor is a nonprofit organization.
Cost Contract-No Fee (Apr 1984)
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(a) The Government shall not pay the Contractor a fee for performing this contract.
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(b) After payment of 80 percent of the total estimated cost shown in the Schedule, the Contracting Officer may withhold further payment of allowable cost until a reserve is set aside in an amount that the Contracting Officer considers necessary to protect the Government’s interest. This reserve shall not exceed onepercent of the total estimated cost shown in the Schedule or $100,000, whichever is less.
(End of clause)
Alternate I (Apr 1984). In a contract for research and development with an educational institution or a nonprofit organization, for which the Contracting Officer has determined that withholding of a portion of allowable costs is not required, delete paragraph (b) of the basic clause.