So, you have a PS4. You have a game you finished. Can you lend it? Can you trade it in? The answer's yes. It's really as simple as that. Now the reason that's a popular question these days is because before the PS4 and the Xbox One came out, there was a lot of worry about the companies having a lot of restrictive policies that stopped you from being able to do that.
They had ideas that sort of tied games to your PlayStation account or your Xbox account that would stop you from lending it to other people. There was all this talk about periodic check-ins online to make sure you were playing games only you owned. There was talk about official retailers that were allowed to buy games and resell games