Sony can ban you from PSN for any reason they want!

[Luiskpx]

Mr Puggsly said:

Corey said:
At least I won't lose all of my games.

I think you lose access to your digital purchases.

https://support.us.playstation.com/app/answers/detail/a_id/1260/~/information-on-banned-accounts-and-consoles

You only lose access to PS+ games and mmos i guess, games you bought normally should be accesible

• Games

  You can: play offline games that don't require any connection to the PlayStation Network.

  You can't: play games that use the PlayStation Network, purchase new DLC, or sync trophies.