I assume you mean the food manufacturer by "manufacturer"...
Packaging supplier has to provide "Declaration of Conformity" according to EU legislation 10/2011 Annex IV. In this document you should find what types of food can be packed (for how long at what temperature) with that packaging. Packaging supplier declares what types of food can be packed based on the migration test results which are carried out according to Annex III of the same legislation. This should cover the due diligence of packaging supplier.
On your side, packaging should be covered under HACCP study, so you should assess the potential risk that can come from packaging. I work in packaging manufacturing therefore I do not know exactly how it works for you, but as far as I can imagine, if you meet the conditions in the "Declaration of Conformity" you are doing your due diligence.
For example you bought vacuum bags from me for your frozen fish fillets and I supplied DoC stating that this vacuum bag is OK to use all types of food for 10 days @40°C. I can only declare that based on my migration tests. If your conditions are within 10 days @40°C I don't see why you have to do migration test. But if your shelf life is 14 days, I (packagin supplier) cannot guarantee that packaging is safe in terms of migration. In that case you can cover the risk by testing my packaging in accredited lab for 14 days. Or you can ask me to do it for you which I will reflect on the price of the packaging.
So you see, for the whole system to work, first you have to tell me what you are packing unless all my packaging is OK for all types of food. Then I supply the correct packaging with DoC. Then you assess the risk of packaging in your HACCP study based on my DoC.
I hope this was clear.