That may be where Broly resides now, but not where Paragus found him. Remember, Broly doesn't start in the new armor. He's in ruined garments. Dirty. Unkempt. Broly is a savage when Paragus finds him. And in the released concept art, Broly is also wearing the collar at that time too. Suggesting Broly has worn it his entire life.
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In the next image of Broly in the armor, his skin seems a bit lighter in tone. As if he'd been cleaned up and given a bath for the first time ever. His outfit is new. All except for the pelt around his waist, which he may refuse to part with. After Paragus gains control over Broly, it's likely that he moved to the seat of Paragus' rule. One thing I want to express is I don't believe that Freeza is going to subjugate Paragus and Broly. At first I thought Freeza might use Paragus to control Broly, but there is something about the scenes shown in the trailer that just make me feel differently.
For instance; Broly exiting the ship and being flanked on both sides by Elite Guard. This is a Royal Entrance. Broly is being introduced as a figure of great importance. As if he were the Slave Prince of the Saiyans. Which also makes be believe that Paragus and King Vegeta may have been brothers after all, and that Broly was a threat to Vegeta's rule. Also, one of the things on the twitter posting from a translated bit by Toriyama, suggested that this movie would be a bit more like a Space Opera. What is more famous a Space Opera than Star Wars? And what does Star Wars have? The Imperial Guard, aka the Royal Guard.
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Robed and masked figures in identical garb that serve directly under the Emperor. Toriyama has used this very same type of image in Super with the Omniking, Zeno. His Guards/Caretakers are all identical and flank him on both sides.
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An almost identical scene was also present in Movie 8 when Paragus enters the throne room to plead with King Vegeta for Broly's life.
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All this leads me to believe that Broly isn't just a soldier and that Paragus isn't Freeza's crony. People also must remember what happened in Revival of [F]. Sorbet's forces, who were the Freeza Faction, were fighting another faction of Soldiers who'd split off. That, I suspect, is the Paragus faction. Sorbet's forces were losing and they were forced to abandon the sector. That was when Sorbet decided to take the chance of going to Earth and using their dragon balls to revive Freeza, since their efforts to find the Namkeians hasn't born fruit.
We can easily see why Broly and Paragus wouldn't have reached Freeza's ears at the time after he was revived, since he was focused solely upon making himself stronger so he could get his revenge. But after the Tournament of Power, Freeza knew he needed to take his time and rebuild his armies in order to fulfill all of his desires. And this is when he finally confronts the issue of the divided Factions, leading to his confrontation with both Paragus and Broly.