In plain English
FAR 52.216-24, Limitation of Government Liability, is a contract clause prescribed at FAR 16.603-4(b)(2), 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 16.603-4(b)(2), insert the following clause in solicitations and contracts when a letter contract is contemplated:
Prescribing reference: FAR 16.603-4(b)(2).
The official text, verbatim
As prescribed in 16.603-4(b)(2), insert the following clause in solicitations and contracts when a letter contract is contemplated:
Limitation of Government Liability (Apr 1984)
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(a) In performing this contract, the Contractor is not authorized to make expenditures or incur obligations exceeding __________ dollars.
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(b) The maximum amount for which the Government shall be liable if this contract is terminated is ___________ dollars.
(End of clause)