It is entirely possible for a Product Backlog to be empty, but that does not mean it has ended. Usually, this is just an indication that bugs have not been logged yet, or the product owner is doing a poor job of planning for additional features.
If you are some one running a product company, and your product has no backlog items, that means you are likely missing vision as to how to keep your product evolving to stay ahead of competitors and reach new markets.
That being said, many agile software projects now run with a product backlog, when in reality this is just a project backlog. Similarly, a release team may be running a product backlog that is actually the release backlog. In these scenarios, it is very common for the backlog to 'end' as it can only live for the length of time up to the project or release completion. The remaining items then fall back onto the true product backlog that spans multiple projects or releases.