It may be available in other customizations of the Android software, however this setting is not available in the Xperia "version" of Android 6.0. You can check if there is any application available in the Google Play store that can lock applications in this menu so they are not closed down when you clear all the recent application list.
Hi @Sony_lovers, sorry for the late reply. I have been out of office due to vacation.
I have not used one myself either, so I'm afraid that I can't give you any suggestions. I tried searching a bit in the Google Play store, but I could only find applications that puts a lock on starting the application.