I seem to remember that Jesus having already died and not needing his legs broken fulfilled an OT prophecy.
Where was this prophecy recorded and what did it say?
Yes, you're absolutely right! Jesus never broke any bones. That's a fulfillment of the prophecy from Old Testament and it's written about in John.
The prophecy that John refers to is found in Psalms 34:20:
Also related to this is the regulations regarding the passover lamb:
Those were the regulations for the lamb that was slain for the passover feast. There are many passages that relate Jesus to the passover lamb. This lack of broken bones is one of these connections. (This regulation can also be seen in Numbers 9:12.)
Before deciding whether the decision not to break Jesus' legs to hasten death was really in fulfilment of these as prophecies, it is useful to discover whether this might have been a common occurrence. John Dominic Crossan says in The Birth of Christianity, pages 543-4, that so far only a single crucified skeleton from first-century Judea has been found by archaeologists: his legs were also not broken.
John's Gospel depicts Jesus at his crucifixion in terms of the Passover lamb, so much so that this Gospel changes the timing of the crucifixion from the day following the Passover feast (Luke 22:15: "And he said unto them, With desire I have desired to eat this passover with you before I suffer") to the day prior (John 19:14: "And it was the preparation of the passover, and about the sixth hour: and he saith unto the Jews, Behold your King!").
The author of John's Gospel chose to alter the date of the crucifixion from that he found in Luke's Gospel, in order to help draw comparisons between Jesus and the lamb sacrificed for the Passover feast, so it is not entirely improbable that, for the same reason, he also wrote the account of Jesus legs not being broken. If so, this is not the fulfilment of prophecies in the normal sense.