Both the sender and the receiver deleted the text after it was sent, but is it still possible that it exists somewhere and that someone can get to it?
It is absolutely not secure. Text messages function essentially the same way email does: your client (phone) forwards it to a server, which then looks up a destination which may be on another network (carrier) and then sends it over where it is held in a mailbox until a phone gets it.

Anywhere along the way it can be copied, retained longer than expected, etc. Lawful interception, unlawful interception, cloned phones, Google+ accounts, etc are all ways a message can end up somewhere unexpected and all that assumes you trust the phone and software on it.

Clear text is compromised text. Always.
