Deathtag

From DoomWiki.org

Deathtag is an old game type played before the influx of multiplayer ports such as Zandronum. The mode is played with two teams of two. One person goes to the enemy base while the other stays at the radiation suit door. The player in the enemy base hits the switch which unlocks the radiation suit in your own base. The player who gets the radiation suit will be teleported to the enemy base, and must run all the way to the scoring line (the scoring line area has a 20% damage sector type, so the radiation suit is needed to survive). The first team to score five times wins.

Wads for this mode can be found in the deathmatch folder on the idgames archive, and notably occur in the first entry of the Unidoom series.