A completely Bulletproof player is potentially an overpowered role. Thus, many times players are simply One-Shot Bulletproof - passively protected from only the first kill that would otherwise resolve on them. Some moderators use Two-Shot, Three-Shot, and so on, but these variants are far less common.
One other variant is a Bulletproof Vest, which is the 'Bulletproof' modifier in item form. The Vest can be passed from player to player (usually at Night), and any player is protected from being killed while they hold the vest.
Some moderators will word their flavor so that Bulletproof only stops kills made with bullets. This allows some roles to bypass the protection; for instance, Serial Killers traditionally use knives to perform their kills. This is not Normal, and is usually considered a subversion for bastard games.
Some moderators interpret this protection such that it only protects against kill attempts, but not arbitrary deaths such as suicides.
This role modifier is considered Normal on mafiascum.net. Bulletproof protects against any kill made by any faction.
Use and Balance
In games with Serial Killers and/or Vigilantes, one member of the Mafia is generally Bulletproof so as to grant the team some measure of protection from being routed at Night. As Townies are not generally Bulletproof, this is only a small respite as the shooter can find a way to claim a guilty result of some kind on the Bulletproof Mafioso.
Serial Killers are commonly one-shot Bulletproof to prevent them from being killed too early by the Mafia. However, they are also commonly given full Bulletproof as well, so the Mafia must think twice before trying to kill the Serial Killer again.
Townies with unlimited Bulletproof are very rare because they can generally only be killed by the lynch. One common breaking combination is Bulletproof+Cop, where the Cop investigates the Bulletproof player. Once the Bulletproof player is determined to be Town, the Mafia cannot get rid of the Bulletproof player until the very end of the game unless they have a Strongman on their team. (It isn't unheard of to have Bulletproof Godfathers with investigation immunity, though...) In addition, if the unlimited Bulletproof role lands in the hands of a skilled Townie, it may be more than the scum can do to avoid getting picked apart with no recourse.
If a Bulletproof Townie is included in the game, some means of handling the endgame in the event that the Bulletproof player lives that long must be considered. Many moderators will simply ignore Bulletproof aspects if a Win Condition requiring a faction to make up half of the living players is attained - in particular, if only one Mafioso and one Bulletproof Townie are alive, the Mafioso will usually be given the win. (Another technique is to place a large limited number of shots on the Bulletproof player to explain why they eventually lose the impasse; after several nights, the Mafioso will have shot them enough times to pierce the protection.)
In terms of power, a One-Shot Bulletproof Townie is less swingy than a Doctor. It is slightly more powerful in a game with no or few other power roles, as it makes it more likely that a particular Townie will be saved from death. On the other hand, it is considerably less powerful in a game with many power roles, as a Doctor can use their power to amplify other power roles via giving them more nights in which to use their power. Fully Bulletproof Townies range from quite powerful to game-crushing depending on who draws the role. A Bulletproof Mafioso (sometimes called a Mafia Tough Guy) is less swingy but less powerful than a Mafia Doctor, and is only a modest power boost. One-Shot Bulletproof is a fair power boost for Serial Killers; full Bulletproof is a considerable power boost.
Bulletproof is not a role that is frequently claimed, and when it is claimed it is generally seen as scummy. From scum, it is partly a justification for why a given player is not being killed by the scum at Night and partly a claim of a role they actually have (scum are much more likely to be given Bulletproof than Town). From Town, a true Bulletproof claim renders its effect useless (scum will not try to kill a player who is likely Bulletproof) while opening its claimant up to potentially being called Bulletproof scum.
This notwithstanding, Townies may claim Bulletproof as part of a gambit. The chance of a Bulletproof Townie existing in the game goes up considerably in Theme games, which makes the gambit more effective in that setting.
Bulletproof Townies may drop intentional Cop or Doc tells, since it benefits them to try to draw the attack overnight. However, care must be taken in these cases to avoid causing the real power roles to become suspicious or counterclaim.