What does it mean the application is completely closed? If you forced it to stop, then nothing will work and never until the application is explicitly launched by the user. In theory, such a forced stop can be done by different shells and manufacturers. Perhaps you should check on other devices.

@ YuriSPb "What does it mean the application is completely closed?" -if you swipe it in the list of applications. With a forced stop, nothing should work, I agree. But when swiping it should, it is written about it in the documentation. I checked it on several smartphones of different brands, it does not work.

@ YuriSPb Yes, indeed. I added the application to the wishlist of the energy-saving system and the push notifications began to come. But how then are notifications sent from other third party apps. And there are not very popular applications, we somehow get notifications from them, but I did not add them to the wishlist.

In some push systems, you can negotiate with a push provider to send high priority push notifications. They, apparently, can bypass such restrictions. In this case, it is not necessary to be a face book. But you have to prove that you need such push notifications. Well, it's not clear which applications you read are not very popular. Perhaps they are more popular than you think, or have agreed with the push provider, or simply have such outdated code that they are not subject to OS restrictions. If you come up with a technical solution, you can try to launch some kind of periodic background task. But this is xs