The linesman's "official" duties are mostly limited to making calls for icing, offside, and conducting faceoffs. They can also blow the play dead for things like the puck going out of play or an injured player, and report infractions that would be worthy of a major, game misconduct, match (and double minor I think) to the referee at the next natural stoppage. Their "unofficial" duties are to discourage altercations and intervene when they do happen.
To answer what I think you might have been getting at, if for some reason both referees are incapacitated during a game, the two remaining linesmen will run the two-official system (role of a linesman and referee combined). The playoffs have a reserve official present at each game (normally a referee) to mitigate this possibility, who will enter the game if an official becomes incapacitated - but will take on the same role (earlier this year one of the linesmen left the game and was replaced by Wes McCauley acting as a linesman). In the regular season, there isn't a reserve official, so they just finish the game with whoever's left if someone goes down. Only in the specific case that both referees are incapacitated does someone who's normally a linesman get to assume the duties normally handled by a referee.
They also get paid less. You can identify them easily since they're the ones without the orange armbands.
