When a bill or pardon or whatever is signed, let's say in the USA, then what exactly happens to the signed document? And what happens if it's misplaced or destroyed?
In the US, signed bills and other documents of import go to the National Archives.
Documents that are misplaced are lost until found.
If the documents are destroyed, the culprit may be the subject of an FBI investigation, which happened to Sandy Berger, Bill Clinton's National Security Adviser.
Note that all public laws are published in the Federal Register. Note that multiple copies of documents are made if they are not secret. The President even signs legislation with multiple pens, for gifts to posterity.