It is the consignor's responsibility and obligation to pack their shipment so that it is suitable for air transportation as well as to take care that the package meets the requirements set by the destination country. These requirements vary country by country. For example, in some countries, packages made from timber must fulfil ISPM 15 standard for handling and labelling.
In case of neglecting these requirements, the shipment can be sent back to the country of departure or can be set into a quarantine. If that happens, the consignor of the shipment is responsible for all the costs.
You can find more information about the requirements for the packaging materials on e.g. Food Safety Agency Evira's web site.