It can be. But the more that fiction is authored in advance, and then used - as secret backstory - to determine consequences of players' action declarations for their PCs, then the more the play dynamic moves away from that which I prefer.
I don't think that (4) is a particularly large or common category, although some of the suggested random rolls to see if climbing PCs drop gear would be an example. The only person in this thread who has mentioned the version of (4) that consists in a room's occupant being rolled for randomly (eg 70% chance the orcs are sleeping, 30% chance they are down the hall brawling with the kobolds) is me, so I assume that that sort of design is not all that common these days.
I don't think any actual examples of (2) have been given in this thread, have they? And are we talking about (a) pre-authoring for purposes of scene-framing, or (b) pre-authoring for purposes of narrating consequences?
(a) is something that I do myself - I will think, in advance, about the way I want to open a session. But (a) is not really feasible for later events in the session, because they have to reflect what has come before, and so can't be written in advance of that actual play.
(b) is what I take to have been the main focus of discussion in a thread on "fail forward". This is one way of negating player agency - for instance, if the GM has already decided that if the PCs look for the mace they won't find it, then (in my view, and given my preferences) action declarations of searching for the mace have been rendered somewhat futile. Or if the GM has already decided that the waterhole near the foothills has been fouled by a dark elf, then - in effect - the players can't fully succeed on a navigation/survival check. Again, by my lights this is a limit on player agency.
A lot of instances of (b) will be the result of pre-authoring secret backstory which is then used as part of the process of adjudicating action resolution. The mace not being in the tower, for example, is an instance of secret backstory that leads to an instance of (b). Another common example might be deciding that an NPC can't be persuaded of XYZ, so that attempts at social interaction by the PCs have a pre-determined outcome (of non-cooperation).
Of course, if the GM changes the notionally pre-authored consequences to reflect player action declarations for their PCs, and whether or not those checks succeed, then we don't have an instance of (2) at all. We have a version of (3).
Examples of the 4.
1) Pre-authored with no player input.
Playing in a world adventure that has no care for the players (forgotten Realms was not made with your character in mind) most pre-made adventures will be of this kind as they don't know which characters are in the party. Characters find their own place in the world and forge out their own goals etc. If they go to city x then there will be thing happening in the city independent of the characters that they can choose to or not to get involved with.
2) Pre-authored taking into account characters, goals desired, what the players want, etc.
Pre-authored, DM adds details that fit the player into the world, where they come from, family. The game is fleshed out based on the interests that the characters exhibit. DO they decide to take up piracy, are they helping the down trodden etc. There may not even be a main "plot" or "story". The world is theirs to do with. Authoring occurs between adventures as well as during.
If they go to city x then there will be thing happening in the city independent of the characters that they can choose to or not to get involved with. But if you have a thief in the party you will make sure the thieves guild is a big part of the city. If they are a cleric of a church then either their church will be in the city or a rival church. The characters interests will be more fully fleshed out in these area. Their family member might be in danger, or need help. Just because this doesn't happen in the way that you want it to doesn't mean that characters interests aren't being taken into account.
3) In the moment taking into account characters, goals desired, what the players want, etc.
The way you like playing.
4) In the moment with no player input.
This is perhaps more common that you think. There is the "random encounter" effect, but also from what you have described anything the DM comes up with that is not directly involving the PC's will come under this. Anytime you don't have a pre-drawn location map and make it up on the spot. If you need to decide if x is in a location and don't tie it to a characters skill. Deciding the weather, the name of the elven princess or barkeep. I have even been in some games where it is clear the DM is just pulling things out of his arse, and yet it in no way related to any of the characters. Any time something happens that isn't part of the "main plots" (if you have them) is in this catagory.
I personally prefer when not everything is so tightly connected to the PC's that it ends up looking like a bad soap opera, with all the co-incidences.
As for scene framing vs deciding outcomes, I don't see things the way you do.
I don't frame in a narrative sense the way you seem to do (if I understand from other threads). I present the situation to the characters as information (no goal presented). They decide how they want to interact with the situation. I decide outcome based on players declared actions (success, failure, unsure). To decide this I know the NPC's temperament, what they want from life, etc. Sometimes that means what the players want to do is impossible (I try to persuade the king to commit suicide, I look for a mace (that isn't there)). But something will happen.
If it is unknown then I will decide the outcomes, choose the skill/skills or probabilities that best reflect the outcomes and roll/have the player roll.
The Pre-authored back ground gives context to inform the nowness of the decisions.
Your option B:
(b) is what I take to have been the main focus of discussion in a thread on "fail forward". This is one way of negating player agency - for instance, if the GM has already decided that if the PCs look for the mace they won't find it, then (in my view, and given my preferences) action declarations of searching for the mace have been rendered somewhat futile. Or if the GM has already decided that the waterhole near the foothills has been fouled by a dark elf, then - in effect - the players can't fully succeed on a navigation/survival check. Again, by my lights this is a limit on player agency.
I do not consider player agency the same as you then. If the player says their character goes into his bedroom to get look for his lost keys, then that is what he is doing. He is trying to discover if his keys are in his room. I lost my keys the other day (my flatmate had borrowed them to get something from the car and put them in the kitchen instead of my room where I thought I had left them) I searched the hell out of my room. I did not find my keys (I did find $1000 that had fallen behind my bed though). They was a successful search, I established that the keys were not there.
If I understand what you are saying you consider any deviation from option 1 to just be a version of option 3? It really makes option 3 so broad so as to be basically meaningless
