Your password will be updated once your reissue request is processed, and the old password will become invalid.
When the old password becomes invalid, you will not be able to use all the services (internet connection, sending/receiving emails, etc.) which use the corresponding ID.

The new password will be sent to you via simple registered mail or home delivery service. 
If the ID is a mail ID, Asahi Net will send your new password to your Asahi Net email address (i.e., @asahi-net.or.jp or @asahinet.jp).