By default, this is what is kept in sync between partner products.
Inventory is synced automatically between the supplier and the retailer. If the supplier sells out then this would be reflected in the retailer's store.
Product Images + Descriptions:
Once a retailer adds supplier products to their store, the images and descriptions will not sync with any edits made by the supplier. Meaning, if the supplier updates the product's description or images, it will not change anything in the retailer's store.
We do this to give retailers the freedom to edit images and descriptions to fit their store's theme/look. If it continued to sync with the supplier, then their potential setup time/effort would go to waste.
If the supplier increases the price, then this will also be reflected in the retailer's store. If the supplier decreases the price, there will be no effect on the retailer's price.