There is an eBay function for Out of Stock setting.

When an item got sold, the quantity will be decreased by its quantity sold.

If you select “ No ”, the system will NOT help the quantity gets back to the original number automatically. If you select “ According to SKU ”, you should go to Inventory > Product Master > Product Maintenance to set up whether an individual item goes with the Auto Refill by using its own SKU. If you select “ Yes ”, the system will help you to perform the function of Auto Refill for the whole eBay account to get back to the original quantity specified in datasheet when a BIN item from this account got sold. The Default Setting will show you the three options for Auto Refill: Yes/ According to SKU/ No. Go to Channel > Sales Channel, click on (gear wheel). You may get your listing record of Relist from Active Listing à Listing History. The sale record of the original ended listing will be cleared. After the ended items auto-relist onto eBay, this listing will be considered as a new listing with a new item number. Keep One Active is a function to relist the ended listing automatically for all listing which has GTC, 3 days, 7 days, or 30 days as setting, ended intentionally or unintentionally. Keep One Active, Auto Refill and Out of Stock

My ebay listings active