Unity uses a unified inbox between voicemail and email. Deleting the email notification of the voice message will also delete the message in your voicemail box.
If you need to recover a deleted message, you can do so either over the phone or on the voicemail website. To access your messages via phone, log into your voicemail and press 3 for “Old Messages” and press 2 for "Deleted Messages". To recover them online, log into unityw1.voip.uic.edu/inbox (you must be connected to the UIC VPN to access this resource if you are off-campus) and select “Deleted Items”.