No, everything is possible.
If you're using an iPhone, you can do the following:
1. Find the voicemail at the bottom of the screen.
2. Scroll down to the bottom of the voicemail list and click the deleted message.
3. Here you can find all recently deleted voicemails. You can play them by clicking on the messages in the list one by one.
4. Now click Undelete to return the voicemail to your regular voicemail inbox.
I hope that you can keep your backups and don't ask how to recover deleted voicemails.
It's possible to recover deleted voicemail on your iPhone if you have no backups after data loss.
Surely, it will be much better if you have created backups regularly. You will get the opportunity to extract data from backup files as well. Most importantly, both common and encrypted data are supported and you can preview contents before recovery.
But as far as I know, we can't get back deleted voicemail on Android phone, but if we want to retrieve deleted voicemail on iPhone, the last hope is data recovery tool, selec voicemail as the recovery data type, the tool will scan iPhone deeply. Preview from the scanning result, then click on Recover to get back deleted voicemail.
There are 3 methods to recovery your data.
First of all, recover from itunes;
Secondly, recover from icloud;
the last and the least expected option is to recover from iphone.
All the three methods are included by joyoshare