The statement does not say ALL of Bible prophecy has been fulfilled. It says: the Bible contains fulfilled prophecy, Which the Bible definitely does contain many fulfilled prophecies. Not all of the prophecies have been fulfilled yet because some deal with the end times. Do I believe all of the Bible prophecies will be fulfilled? Yes.
The scriptures teach that there was a point of time when all prophecies would be fulfilled. The scriptures is the inspired Word of God known as the Bible, Which consists of the Old Testament and New Testament. The Bible teaches us that God cannot tell a lie. Therefore, If the scriptures teach that all of the prophecies in the Bible were fulfilled then all of the prophecies have been fulfilled.
I'm just going to make a list of all of them. Most of these verses are self-explanatory.
For every "fulfilled" prophecy I could give you ten failed ones. So that whole "all the prophecies will be fulfilled" thing is itself a failed prophecy.