Syncee by default doesn't import out of stock products from your supplier.
But with a small tweak, you can import these products to your store if you wish.
Here is how to do it:
1. Set up your import task, and DO NOT map the inventory and the Shopify tracking for your products in the mapping.
2. Run the upload.
3. Go to the task again after the upload is complete and set the inventory in the mapping and the Shopify tracking if you want to track the stock.
4. In the Basic Mapping Settings choose to null those products which are out of stock.
5. Make sure the Inventory is marked under the Update options settings.
6. Run an update.