Do porn blockers work when the app is closed?

A system-level filter keeps working with the app closed, because iOS applies it and no app process is involved. A filter inside a blocker’s own browser stops as soon as you open a different app. DNS filtering works across apps but drops when the network changes.

Where can a porn blocker do its filtering?

Three places, and only one is unaffected by closing the app.

Inside the blocker’s own browser. The app ships a browser and filters what that browser loads. Opening anything else gets around it. Force-quitting is not even required.

At the network layer, through DNS. The phone looks up addresses through a server that refuses to answer for certain sites. It works whichever app you are in, and it drops when you change network or when something else takes over the connection.

At the system level. iOS applies the restriction itself. Nothing has to be running, so there is no process to close.

Which failure belongs to which method is covered in three ways to block porn on a phone.

How can you tell which kind of blocker you have?

Restart the phone and test the block before opening anything. If it holds, it is not living inside an app. If you have to launch a program first, or the app calls its own browser the safe one to use, closing that app is enough to get around it.

Can any iPhone porn blocker be impossible to bypass?

No. None of the three is unbypassable, and a listing that claims otherwise is overstating what an iOS app is allowed to do. A system filter set through Screen Time can be switched off by anyone with the Screen Time passcode. Why that matters is in why porn blockers stop working.