Hildibrand's story is short (only 2 quests) and provides a significant amount of context to the Wolf Burglar's crimes.
Inquiring around Kugane reveals that he's revered as a Robin Hood like figure, stealing from corrupt businessmen and giving to the poor. The party comes to the consensus that questioning him will lead them to Yojimbo and the stolen Soboro Sukehiro, so (along with the Dead Gentle Man in tow) they pay a visit to the Wolf Burglar in prison. After typical Hildibrand shenanigans, the Dead Gentle Man is left impersonating the Wolf Burglar in his cell while the Wolf Burglar absconds with the party. After making more inquiries in Kugane's underbelly, they come to the belief that Yojimbo is pursuing the Ame-no-Murakumo (yes, Susano'o's colossal blade) and give chase to the Ruby Sea.
Upon arriving there, some idle conversation gets the Wolf Burglar to reveal his backstory: he was after the Soboro Sukehiro and that alone, and his rash of hits were designed solely to draw out the weapon. It was a keepsake from an unnamed samurai who fled the Imperial occupation of Doma and effectively adopted him as a foster son, only to be taken when he died due to Akebono (the merchant) worming his way into his finances. The party then inquires around Sakazuki asking about Yojimbo, eventually sussing out Daigoro who leads the party to Yojimbo. Through Hildibrand shenanigans, the Wolf Burglar gets the Soboro Sukehiro back, but absconds when the Sekiseigumi show up having figured out the ruse and intent on returning him to prison. Shigure is carted off to prison for his part in the fiasco, though Hildibrand and Nashu vow to free him due to the extenuating circumstances making his unlawful actions justifiable as they were for the greater good.
It was pretty obvious that Akebono was not entirely on the up-and-up from the beginning (he tried to sell Hildibrand as a statue and a live qiqirn for human consumption). The Wolf Burglar being Kugane's Robin Hood puts his crimes in a new light, but samurai are supposed to be Lawful Neutral... so the Sekiseigumi insisting on hauling him in anyway is hardly surprising.
Oh, and the shenanigans led to Shigure regrowing his hair with a tonic Nashu supplied as well as donning a new outfit to move about incognito. Didn't fool the Sekiseigumi for a second, though.