is it illegal to throw away someone's license/ID?

Unknowingly, it's not punishable. Knowingly, it's a crime.

Fact is, the ID isn't even the property of the person it is issued to, it is property of the state issuing it, given to the person to identify themselves to the authorities.

The employer and any person finding an ID is usually obligated to turn it over to the authorities. Merely having it in their office but not knowing it is not a crime, unless they should have known (like, in a chemical plant, you leave all your items in a locker and wear coveralls) it is on their premises. If they don't know and should not have known there is an ID in a box of "junk" they might get off the hook for tossing it.

The arrested could have prevented the loss of the ID by informing the authorities during being held that his ID was at the company (possibly putting them on notice) at which point the police might get all the items as evidence, or having a next of kin or attorney go and retrieve the items at the company.