Pillagers have an Inventory nbt tag which is not used at all, especially in survival since pillagers are never capable of picking up items from the ground. This nbt tag can be seen by using the /data command on a pillager:

/data get entity @e[type=pillager,limit=1] 

After using the command, the Inventory nbt tag can be seen at the very end of the following data of the specific pillager.