With this flag on, go up to any NPC and hit Y to remove them from the map. Any screen transition will reset any “removed” NPCs, but you can remove them again.
NPCs are not limited to just townspeople. You can remove monster NPCs, various random objects, locked doors, and even invisible barriers.
Note that any removal of boss NPCs that result in skipping the fights entirely will also bypass any rewards resulting from that fight event. It is possible in some cases to soft lock a seed if you have skipped these fights but are required to acquire certain Espers, kill certain bosses, or complete a certain number of checks.
Y NPC provides access to:
All of Magitek Factory: remove the NPCs blocking the entrance when gated by Celes. You can then remove the Ifrit & Shiva and Number 024 NPCs as well, skipping those boss fights entirely.
All of Zozo, in both worlds, including Mt. Zozo and its reward. For Mt. Zozo, remove the NPC door that you normally need to buy Rust-Rid to open. For Zozo Tower, remove the Dadaluma NPC blocking the last stairwell to skip that fight. In Zozo WoR, remove the sleeping NPC blocking the doorway to enter Zozo Tower. If you are trying to solve the clock puzzle, this will give you access to the NPCs that give you hints. Note that in character gating mode, there will be no reward at the top of Zozo Tower if you haven't recruited Terra.
Figaro Castle Throne and Engine Room in the WoR, and subsequently Ancient Castle. Remove the NPC in South Figaro Cave WoR that blocks access to the tunnel leading to Figaro Castle. This NPC normally disappears after you have recruited Edgar. While in Figaro Castle, you can remove the blocked main door to go north to the beds, shops, and throne, even while the castle is buried - that is, before you have completed the Engine Room check.
Narshe WoR: remove the locked doors leading to the Weapon Shop and Cursed Shld. Other locked doors in Narshe can also be removed - notably the treasure hut.
Floating Continent: remove the AtmaWeapon and Nerapa NPCs to get the final reward without fighting either boss spots.
Albrook dock in WoB: remove the Magitek NPC blocking the way to get access to the dock chest in WoB
Imperial Camp: remove the “NPC” when facing the hit/kick/leave chest, which allows you to open the chest without any cutscene.
Cyan's Dream, the Lump of Metal chest: Start on either the left or right tile (not the middle). Push Y while facing the chest. Then, move one tile over (to the middle tile). The chest will follow you to block your path. Face the chest, then push Y. Then return to the original tile you started on, and go up. The chest will not follow you.
Opera House WoB: remove the locked left side door which leads to the catwalks; no need to flip the right side switch.
South Figaro WoB: remove the NPC blocking the way to eastern exit.
Potential soft locks or other unrecoverable checks:
Imperial Camp: remove the Kefka NPC during the chase sequence, or remove the check reward NPC during the 3 battle sequence.
Collapsing House: in character gating mode, remove the NPC that normally blocks the way into the collapsing house (if you have recruited Sabin you won't be able to do this). You can acquire the chests and fight the 2 MIABs. Note that walking on the doorway tile into the house will start the timer, if event timers are enabled. The kid NPC won't be in the house if the Tzen sequence outside didn't happen, so you will need to either start another timer (e.g. Opera House) or find another way to get rid of the timer, otherwise you will game over. If you hit A while facing where the kid NPC would be, the game will freeze.
Phantom Train: remove the ghost NPC that you need to fight to exit the third train car.
Magitek Factory: remove Cid before the mine cart ride, leaving you stuck in the save point room.
Magitek Factory: remove the Ifrit & Shiva and/or Number 024 NPCs, then complete the cart ride.
Doma Siege: remove the boss NPC.
Floating Continent: remove the first check reward after dropping down from the airship. Remove the AtmaWeapon NPC and then complete the Floating Continent Escape check.
Figaro Castle WoR: remove the locked doors and leave the castle, while the castle is in transit to/from Kohlingen or the Ancient Castle. You'll appear on the world map but the castle will still be buried, making it impossible to re-enter.
Lone Wolf: after the check reward NPC and Lone Wolf are separated and both hanging on the edges of the cliff, remove the invisible barrier blocking the way across the bridge, then exit and re-enter this screen. You'll need to remove the invisible barrier again. Both the check reward and Lone Wolf will appear in their original positions. Talking to either one may put you out of bounds after the resulting cutscene, depending on which tile you were standing in.
Floating Continent: remove Ultros on the airship deck.
Auction House: remove the NPC that eventually buys the Imp Robot, then start the auction and have the Imp Robot be the item. The game will eventually freeze during the cutscene.
Solitary Island cutscene: remove the invisible barrier in Cid's house, which leads to the raft cutscene where you ride it away from the island towards Albrook. The airship will be stuck on the island after the cutscene.
Other notes:
Several boss NPCs can be removed, but going in and out of the screen will allow you to reset the NPCs so you can fight them. For example, in Opera House WoB, you can remove Ultros on the catwalks. You'll have to exit the catwalk screen to reset the NPC - go back to the left hand stairwell, then back to the catwalks. In Ebot's Rock, you can remove Hidon in the final room. Going back to the teleporter will reset the NPC.
Owzer's House WoR: the 3 cycling doors can be removed.
Mt. Zozo: remove the flowers and letter in the room just before the check reward.
Kefka's Tower: while the Y button is used for switching parties, you can sometimes remove the 4T weights that you push onto the switches. Re-entering the screen will bring them back.
Magitek Factory: remove the invisible barrier after hitting the switch in the tube room and leave the factory. The “shaking” effect will be carried into Vector and other maps, and music transitions won't function properly.