Other then the OP seeming to think like your average kid on the playground(one up mentality), this is a good concept but it would have to be done right.
First of all a stalker like event is already in teh game with decon or what ever his name is, he is basicly a stalker and you can see him in several events before you actually meet him, Anyway for a hostile stalker or assassin it would have to be played out well.
For example randomly getting shot at by a long range laser weapon from a bridge or tower only to find there is nothing there when you get there or just have enough time to see a shaddowed figgure pull a stealth boy before vanishing.
That would be a great event to start a stalker quest line, but it would have to be one of many instances of near miss or direct hit confrentation. Having to deal with an enemy playing in the sniper play stile is a fear inducing state.
Other events could be set if you go to sleep in dangerous areas like sleeping in a random bed outside of a settlment only to wake up with a note in your inventory and a poisoned debuff.
The problem with a stalker/assassin is simple, rarely if ever is a confrontation with one fun. Sure it may get rid of the guy but an assassion working from range hired to kill you or make your life hell, that doesn't make much of a fight unless the fight is on their terms in which case the player may fill powerless which in a game like fallout 4 is something needed from time to time, the thought that this one guy, is your equal able to keep up with you do harm to you and always get away is disimpowering to some one playing a virtual demigod. (basicly every player character ever in an RPG)