It sure is possible, sometimes you might notice if you restore your phone from backups or factory settings deleted texts will suddenly appear again. Deleted messages an similar data are only marked as free space to be written over so all messages and pictures and so forth are still there until they are written over.
For text messages it depends on where they are stored be it the phone or sim card, you need a sim card reader and for the other im not sure but its probably some form of program that recovers deleted data. you also need a program to recover deleted data from the sim card using the sim card reader.