Yes it is advisable to notify a person(or a complete team) for any failure, success, rejection, approval in every term.
suppose you sit in an exam and you did the basic things, how will you come to know that you are pass or fail? someone have to notify you that you score this much in the exam,
There is kind of Action and Reaction, you did something and everyone who is concerned with the thing should be notified about the action.
if there is a mail undelivered we got an error (notification) in gmail, that the mail is not delivered to the recipient. so user is informed(notified) about the failure if gmail don't provide such notification how would user know that his mail is not delivered.
and what you have said in your comment
For example, if I share to you a document and I remove it later.
system should notify that the document has been removed by user, by doing this both will be informed about the action.