A soul who dies in Hell, as all who travel there swiftly do, becomes a Togabito- a Sinner. After each death in Hell, a Sinner's body is simply restored, to be destroyed again and again until their will to reform their body is lost. Half-physical, half-spiritual chains manifest to bind their souls directly to the pits of hell, appearing attached to and within their bodies. These chains make it all but impossible for nearly all Hell-binded souls to leave the plane of torment.
As a Sinner dies, reforms their body and resists the shackles and torments of Hell, they steadily acquire spiritual power utilized in all but futile conflict with the Kushanada- the enormous, Hollow-like wardens of Hell, mindless beasts who slaughter and consume sinners over and over. A Togabito who somehow escapes Hell is also hunted by these beasts if their face is ever exposed in other worlds, albeit the most powerful of Togabito have managed to exist in other realms for short periods of time -without- being killed and returned to Hell by the Kushanada.
There is no military, society or organized order for the Sinners; in Hell, there is markedly less order than there is even in Hueco Mundo, for even in killing another Sinner one's enemies will always return to embattle them again. Togabito do as they wish and work together only when they please- a necessity only demanded to fight off the Kushanada.
Whereas most Togabito fail to overcome the wardens of Hell, a simple and hard truth for these damned souls evidenced by the fact they are almost never seen outside of their eternal prison, there are a rare few who manage to fell Kushanada on their lonesome and breach through Hell's clutches into a fleeting, but triumphant freedom.
Revival: A Togabito who is killed will simply reform their body deep within Hell, and may similarly reverse any injury- albeit slowly. However, each death revives the Sinner a little deeper in Hell, making the journey above and beyond significantly more difficult. (A Sinner who dies is unable to play for a week, then respawns as they were before dying; they can't train in this time. I suggest a passive that can be bought which shortens the respawn time.)
Chains: In time the chains bound to a Sinner's body and soul become extensions of their very being- one they can manipulate at will. As they spend more time in Hell and endure more deaths, their power increases, and with it too comes command over these bindings. Sinners may cause their ordinarily broken-off lengths of chain to manifest into much longer forms for short periods of time, to be used offensively or defensively as tools; the strongest of Sinners utilize these like prehensile appendages. Each time a Sinner dies more chains are bound to their souls to drag them deeper into Hell upon their next death, but almost all of these bindings are normally invisible and cannot be seen normally unless manifested. (I suggest a technique for this that improves offense/defense in all action while chains are active, consuming reiryoku until it's deactivated. Graphics optional- but chains appearing around the user would be cool.)
Abilities: Any powers a Sinner had before being sent to Hell are retained by them in the afterlife. Hollows and others who become Sinners keep their abilities exactly as they were- but they are changed in appearance and often in effect, gradually becoming stronger with their continued existence in Hell's pits. But such Sinners are no more advantaged than humans sent directly to Hell, for Togabito who did not already possess powers will develop their own abilities utilized for combat in Hell.
Examples of Sinners in combat:
Kokuto (Chains, Weapon manipulation/conjuration, barriers): https://www.youtube.com/watch?v=MFTc-l22ick
This wiki page is also very informative regarding what Togabito are capable of in the canon: http://bleach.wikia.com/wiki/Togabito
In essence, Sinners in BRT would be respawning antagonists with unique abilities. An apparent but not quite confirmed theme however is that Sinners have no releases- their 'immortality' is balanced out by this lack of any equivalent to such, as well as having a respawn time penalty.
For their techniques, I suggest a tree with three paths. Hellfire, Chains and Witchcraft; the former is the manipulation of flame, imitating Hell's inner inferno and twisting it into offensive conjurations. These techniques would be exclusively nukes and destructive reiryoku-based attacks. The highest Hellfire technique would involve producing images of the user composed of nothing but flame, which can detonate at will.
Chains, on the other hand, are more complex-
1st technique- Chain manifestation. Conjures chains attached to the user which are manipulable and almost unbreakable, used to attack others or intercept blows. Strength/Defense raised by a flat level of stat points determined by the 'Hell's Chains' passive.
2nd technique- Chain pull, a technique which pulls the soul of the Togabito and their body along a single length of chain in an instant, moving them at rapid speeds; a flash-step equivalent. However, this can never move the Togabito upward, and if they are airborne usage of it will pull them down to the nearest physical surface.
3rd technique- Chain bind- this technique roots the Togabito themselves in a location as all their chains manifest in unison, but also extends the chains to temporarily bind and envelop all those near them, completely immobilizing nearby foes as well as the user.
Having all the chain-related techniques as well as maxed-out 'Chains' passive allows the Togabito to conjure and manipulate a single weapon of their choice, capable of contending with released zanpakuto as a melee (and ranged if swung/thrust by chains) weapon.
Witchcraft would consist of purely non-offensive techniques that tamper with both the Sinner's existence and that of anything in contact with their chains. This is a largely supplementary tree;
1st Technique- Fissure; through the force of their spiritual power and binding to Hell, the Sinner twists a flux in Hell's space that allows them to temporarily slip into other worlds. If they do not keep their face hidden at all times however a Hell gate will manifest and forcibly pull them back into Hell.
2nd Technique- Revival; excites the binding powers within a Togabito's chains, temporarily exposing them to the entirety of the pull towards Hell their spirit normally exists in defiance of. This kills the Sinner instantly wherever they may be, and manifests them in Hell- albeit this respawning process takes only half as long as normal.
3rd Technique- Reversal; allows a Togabito to forcibly reverse wounds they have suffered, restoring lost flesh in a very gory and visceral process that is painful to undergo. Rapidly heals but stuns the Sinner using this technique; powerful Sinners using this technique are set aflame for its duration, suffering but bettering through the cleansing, summoned flames of Hell.
The above are just suggestions for BRT's in-game substance; it'd be really nice if, as was the case with some releases, prominent player-Togabito could get custom techniques added as well as their own special abilities.