Note that deleting the listing will not delete the ASIN page (catalog page). It will always be there.

If you plan on never restocking, then the best advice is to delete the listing.

If you plan on restocking, there is no need to delete, unless you wish to change the SKU or similar in the future for your particular inventory management (tracking expiry dates, batches, etc.) Otherwise, just leave the listing with a qty of 0, then when you restock, just reset the qty to reflect what is on hand (or ship to FBA, if that's what you are using).