PlayStation 2 license problems how do they deal with it?

That there are numerous games where there was too much music, such as DefJamFightForNy or Nfs mw etc. This game can't get remakes due to license problems.

how do they deal with these licenses? I mean ps2 is not like ps4 where you can update / remove game content with updates?

because such music licenses are bought for certain periods but is forever on ps2

The licenses for such products are not temporary, but linked to the product. While it can be limited in time for manufacture / sale, once it is sold it remains a valid license.