A Rolex can change hands without its warranty card. That absence doesn't show that the watch is stolen, but it removes one document buyers often use to compare the serial. Look for other records before deciding.
Ask what documents remain
A dated invoice, service receipt, insurance schedule, or prior sale record may identify the watch. Compare the serial on those documents with the engraving. Ask how the seller acquired the Rolex and whether they can provide a written receipt that names the serial.
Search the actual serial
Confirm the number on the physical watch and run a stolen-status check before payment. A result with no match only covers the records searched at that time; it doesn't replace the missing warranty card or prove the seller's title.
Use an inspection for authenticity
A database search cannot authenticate a Rolex. If the lack of papers makes you uncertain about the watch, arrange a physical inspection by a specialist before closing the sale.
If there are no papers, no inspectable serial, and no written sale record, you have little to verify. Waiting or choosing another watch is reasonable.
Start With the Watch's Serial
Compare any remaining documents with the physical Rolex and save a dated search result.