Two separate things that sound like one
Liability is what a carrier owes if goods are lost or damaged in its charge. Insurance is a policy a party buys to be compensated for a loss. A shipment can be carried by a fully compliant, properly insured carrier and still leave the cargo owner substantially out of pocket, because the carrier's liability and the value of the goods are not the same number.
This is the single most useful thing to understand about freight risk, and it is why "is it insured?" is an ambiguous question. The precise question is whether the goods are insured, and by whom.
How liability works for international road carriage
International road carriage between countries that are party to it is governed by the CMR convention, which makes the carrier liable for loss or damage occurring between taking over the goods and delivering them — subject to defences and to a limit calculated by weight rather than by value.
Because the limit is weight-based, it protects dense low-value goods far better than light high-value ones. A pallet of electronics and a pallet of steel of the same weight attract the same limit and are worth very different amounts.
Where the gap usually appears
High value per kilogram is the obvious case. So is anything with a consequential cost larger than the goods themselves — a component whose absence halts a line, an item that cannot be replaced within the season.
Defences matter too. A carrier is generally not liable for loss arising from inherent defect, from insufficient packing by the consignor, or from circumstances it could not avoid — which returns the question to how the goods were prepared, and is one reason the packing standard is a commercial matter and not only a practical one.
What to establish before a shipment moves
Whether the goods are insured, who holds the policy, what it covers and to what value, and whether the agreed commercial terms put that obligation on the buyer or the seller. Under most Incoterms rules neither party is obliged to insure at all, and the risk simply sits with whoever holds it, uninsured, unless somebody has bought cover.
Nothing on this page is insurance advice and none of it describes any particular policy. What cover is appropriate for a specific consignment is a question for an insurer or a broker, and the position under a specific contract is one for the parties and their advisers.