"your (lowest cost) subcontractor"
Stop pretending the expensive commissions you pay to third party sales people, management or shareholders will somehow result in better quality while they continue to use the cheapest resources available.
Your suppliers will meet their contractual obligations. Experienced suppliers already have the get out of jail clauses included in the contracts. If your contracts don't clearly specify responsibility and how risk/damages will be assigned in the event of data loss, your company probably carries a significant proportion of the third parties risk.