Inventory is kept in sync between the retailer's and supplier's stores. If the product is sold out on the supplier's store, then it will also appear as sold out on the retailer's store.
By default, there's a stock buffer of 5 in place for all partnerships. Carro will check the supplier's inventory levels every hour and display products as "out of stock" on the retailer's site when inventory sells down to 5 units to avoid overselling.
The supplier controls the inventory levels and ships the products when something sells through the retailer's site. The retailer does not handle, purchase, or control any inventory as part of this partnership.