Despite various reports in the media, if installed, P.T. will remain safely on you PS4 system. Konami reached out to VG247, mentioning that it is not automatically deleting the demo off of consoles. The company did reiterate, however, that if the game is not already installed on your PS4, it cannot be downloaded or re-downloaded.
If you don’t have the game already on your console, then you might want to keep watch on Allison Road, a fan-made, spiritual successor of P.T. that is currently in development.