In plain English
FAR 52.249-4, Termination for Convenience of the Government (Services) (Short Form), is a contract clause prescribed at FAR 49.502(c), 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 49.502(c), insert the following clause in solicitations and contracts for services, regardless of value, when a fixed-price contract is contemplated and the Contracting Officer determines that because of the kind of services required, the successful offeror will not incur substantial charges in preparation for and in carrying out the contract, and would, if terminated for the convenience of the Government, limit termination settlement charges to services rendered before the date of termination:
Prescribing reference: FAR 49.502(c).
The official text, verbatim
As prescribed in 49.502(c), insert the following clause in solicitations and contracts for services, regardless of value, when a fixed-price contract is contemplated and the Contracting Officer determines that because of the kind of services required, the successful offeror will not incur substantial charges in preparation for and in carrying out the contract, and would, if terminated for the convenience of the Government, limit termination settlement charges to services rendered before the date of termination:
Termination for Convenience of the Government (Services) (Short Form) (Apr 1984)
The Contracting Officer, by written notice, may terminate this contract, in whole or in part, when it is in the Government’s interest. If this contract is terminated, the Government shall be liable only for payment under the payment provisions of this contract for services rendered before the effective date of termination.
(End of clause)