Whilst a parcel is in the courier’s possession, they have legal responsibility over it and owe the sender, who paid for their services, a duty of care. However, as they are providing a service under contract, the customer will be bound by the terms and conditions which were accepted when the service was initially taken out. Such terms will likely cover the position with liability in the event the parcel is either lost or damaged.
Often, couriers limit their liability to a specific amount, regardless of the value of the item. They basically state that if the customer is prepared to use their services, they are agreeing to the courier only having liability up to that amount. If the customer is not happy with that basic level of cover, they simply do not have to use that specific courier. There is, however, often the option for the customer to purchase extra cover for additional protection. This is like getting insurance, up to a specific amount, or for specific eventualities, which provides extra cover for the items. For example, it can increase the amount that is covered and also cover more specialist items, which would ordinarily be excluded.
If the customer did not purchase such extra protection, the courier will still only be liable up to the minimum amount they cover under their terms and conditions of use. That would be the case even if they were in some way at fault for the loss or damage. That is because they would have contractually excluded their liability and the customer accepted that exclusion by agreeing to their terms and using their services. Had extra insurance been purchased, the limits of their liability would have increased up to that amount and the goods would have been protected better that under their basic cover.