Does a voice text get deleted? I sent a voice text to a friend, but didn't save it on my thread. And it was automatically deleted after the default 2 minutes. 

Does the voice text stay on the recipients messaging thread until they have a chance to hear it, and then decide weather or not to keep it? 

Basically, do remote deletes on their thread happen once it's been deleted on my thread?
There is a setting under Settings -> Messages -> Audio Messages section. There is an "Expire" option, where you can select 'after 2 minutes' or 'never'. That is why it disappeared from your message thread.

Your friend will have it in their message thread until they listen to it, and then the phone will either remove it after 2 minutes or keep it, depending on what their setting is.

So to be clear: what you see in your message thread isn't in any way linked to what your friend sees in theirs. If your message gets delivered to two Macs, three iPads and one iPhone, this concept applies to pictures as well. Each device that has the message handles deletions independently of the others.