I agree with Allegiance.
The PJI's likely do have some other function than what is mentioned. They are after all one of the largest structures and can easily dwarf even the largest frigates. That does perhaps mean that while they can inhibit phase jumping, they could also have the ability in general to warp-space time. Really it depends on how phase space works. We can assume however that to do such a thing, you have to make sure that planets are aligned in such a way as to use their gravity to throw off your jump. This means that PJI's most likely warp space-time around targeted objects. Now, while this can be used to slow PJing, it could also be used as a weapon, perhaps even reducing a ship to a small black hole. That is a weapon.
I'm thinking that they left due to their technology running amuck... Since then, they probably became very secretive and will no longer interact with other races. This does give me an idea though... Perhaps they were not the problem. Perhaps they gave their hyper-advanced technology to others to be generous and those inferior races were the ones that corrupted it and turned it against the Provetiens. Perhaps this inferior race was the Vasari. Perhaps the Provectiens gave the newly discovered Vasari the technology to create super-nanites that could work faster and function in any number of ways. Due to the nature of the Vasari, they wished to turn it into a weapon in the weapons lab on Kron. On that day, they changed the code of the nanites, but the abilities the nanites had were the same. Instead of repairing ships, they began to destroy them. Instead of healing wounds, they began to make them deeper. Instead of mining for ore, they ate planets. And that started the running of the Vasari.
Obviously the Provectiens wanted to stop the process, but could likely only fight the nanites one-for-one, yielding no clear winner. As a response, the Provectiens created the Tutero (from the latin "attero" meaning destroy and "tutela" meaning guard), a monstrous machine capable of yanking areas of space clean out of the universe. This three-armed machine would hover in orbit around a planet and would wait for enemy vessels to come within a 16000 kilometers of it before unleashing its awesome power on entire fleets.
As the Provectiens fled to another galaxy due to the shame of having destroyed the Vasari race (or so they thought) by attempting to be generous, they left behind defunct tuteros that were eventually discovered by the Vasari. Now, though they did not know how they worked, they Vasari did discover that they could aim it at ships and could prevent them from jumping out of the system. For this reason, they called them Phase Jump Inhibitors. The same applies to the Advent and TEC (which likely discovered the tuteros before splitting a thousand years ago...)
As for being a nanite cloud. I don't think it would be much of a cloud. Think giant space-borne metallic organism. The nanites would more or less be alive. After all, they fit every qualification of it minus the genetic code. As the colony of nanites grew, it became self-aware and sentient. As it continued to expand, it began to have interests and goals until it had enough that it could begin to fulfill those goals when it found a ship in a hangar bay on the Kron laboratory. It infected that ship and then recreated it. Now, the Vasari thought that by self-destructing the laboratory, they could stop the infection, but that one ship escaped the destruction of the rest.
It proceeded to dock on board a capital ship and continued the infection. With nanites already in the ship, it merely rewrote the code of the nanites on board as it met them, quickly conscripting an army. Within days, the nanites had consumed the Kortul and in the process had gained information about how it worked. It had discovered phase technology. By reforming into the Kortul, it left Kron and went to another central world. That world was also infected until a small fleet was assembled of the nanites.
With more and more worlds falling silent, the Vasari dispatched the Dark Fleet to deal with the problem. Unfortunately, it is hard to shoot at something that can just reform after being hit. All the nanites had to do was hit a few shots home on the enemy vessels before the infection would take hold and would win another ship for the nanite fleet. One Kortul survived though. Taking only one shot from an enemy fighter, it was able to stop the infection with only part of its hull destroyed. As it was, it limped back to another world where other Vasari found it and the crew driven mad from having seen each other and the ship they lived on attempt to absorb them into one single cohesive entity.
What do you guys think? Seems to make sense. If you are wondering about the form I used, each one was a bit of a story, but the double spaces represented addressing a different paragraph of Allegiance's post...
Btw, we need to call the nanites something so we can refer to them without having to clarify which nanites we are talking about...