Adobe form Validation

The required property is only used when the file is submitted. You said you want the user to send the form back to you. At that moment, if they use a button set to submit the form, it will validate the those fields and not allow the form to submit if they are not filled in.
If you want to also perform this validation when the file is saved you will need to use a script, like this (paid-for) one I've developed: https://www.try67.com/tool/acrobat-validate-required-fields-before-printing-or-saving

Note it can't actually stop the file from saving, but it can force the saved copy to be blank, and to display an error message to the user.

A user may have many good reasons for wanting to save his form and finish filling it in later.
So rather than trying to prevent this, an elegant programmer should simply alert the user via an alert box.

See these topics:

https://community.adobe.com/t5/forums/searchpage/tab/message?filter=location&q=valid%20required&advanced=false&location=forum-board:acrobat