I think the information goes into hiding. By irreversibly deleting bits on your computer, you have to produce heat exchange, the entropy rises and that is a sign that the information you once had is now part of the statistical thermal noise and not recoverable any more by macroscopic measurements.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition