To hide price for unavailable products, go to Catalog Settings > Inventory Manager and check the Hide price when unavailable checkbox:
Once enabled, it will hide the product price when the inventory is set to zero.
Force price display per product
To exclude a product from the inventory rule, go to the product edit screen and find the inventory box:
Once you check the Always display price checkbox, the price will show up even with an empty inventory.
Exclude products from inventory filter
In Catalog Settings > Inventory, you can also check the following checkbox:
Do not filter the Always Display Price products – The inventory filter will show the products with the Always Display Price checkbox checked as available.