Important: Stalker and Shadow Stalker are fundamentally different enemies!
Killing bosses in the starchart marks you for death by the Stalker (1 mark per boss). When marked, you will receive an inbox message like shown here and the Stalker has a small chance of spawning in your missions to kill you (chance is increased if playing with squadmates who are also marked). Stalker is immune to all warframe abilities so make sure to carry at least one well modded gun. Upon completion of the Second Dream, subsequent Stalker spawns will be Shadow Stalker, a weaker version that has sentient damage immunity mechanics (which can be reset by void damage, Umbra’s radial howl, etc.) but is not immune to abilities. Stalker drops are listed here and Shadow Stalker’s here.