Is the mother obligated to compensate the owner of the carpets that were lost due to the airline company, given that the loss of the carpets occurred in 1992, the compensation was requested 6 years later, and the mother's financial situation has improved now after 17 years?

Your mother is not obliged to guarantee the damaged luggage and carpets, because her possession of them was as a trustee, and a trustee is not liable for guarantee unless she was negligent in their safekeeping. Thus, there is no guarantee on the part of the custodian, and any property damaged while in the possession of a trustworthy person, without transgression, incurs no guarantee. The airline company is responsible for the loss of these items, and the questioner's mother has no right to demand anything from your mother unless compensation comes from the airline company.