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I know right? Quickly setting the stage: a BBEG is standing toe to toe with a fighter. The fighter swings with their sonic sword and crits. Rolls are made the BBEG is deafened... permanently. Then before the BBEG could retaliate they are blinded by a caster. This is a two parter.
1. So if the fighter is grabbed or otherwise flatfooted to BBEG would BBEG get sneak attack damage? I think this question equally applies if a rogue is attacking someone invisible OR if they are in complete darkness and somehow the target gets flat-footed. Do they get precision damage?
By RAW it looks like the BBEG would get sneak attack damage, but it was contested and I wanted to see what people's thoughts were RAW vs RAI.
2. Let's say the fighter moves back 5ft the end of their round... Being Blinded and Deaf can the BBEG SEEK out? I imagine it'd be slow and difficult randomly guessing squares and all that. Sounds like the fight is over at that point, but for completeness sake curious on thoughts RAW and RAI.

SuperBidi |

I know right? Quickly setting the stage: a BBEG is standing toe to toe with a fighter. The fighter swings with their sonic sword and crits. Rolls are made the BBEG is deafened... permanently. Then before the BBEG could retaliate they are blinded by a caster. This is a two parter.
1. So if the fighter is grabbed or otherwise flatfooted to BBEG would BBEG get sneak attack damage? I think this question equally applies if a rogue is attacking someone invisible OR if they are in complete darkness and somehow the target gets flat-footed. Do they get precision damage?
By RAW it looks like the BBEG would get sneak attack damage, but it was contested and I wanted to see what people's thoughts were RAW vs RAI.
2. Let's say the fighter moves back 5ft the end of their round... Being Blinded and Deaf can the BBEG SEEK out? I imagine it'd be slow and difficult randomly guessing squares and all that. Sounds like the fight is over at that point, but for completeness sake curious on thoughts RAW and RAI.
1. If I remember correctly, it was something in past editions. You no more need to see your opponent to Sneak Attack them. So the BBEG would get the Sneak Attack damage.
2. As the BBEG is deprived of both its precise and imprecise senses, it only has its vague senses to work with which are not supposed to give a precise positioning. So in that case the BBEG is forced to strike at random. It can try to use touch, by moving around trying to move onto the Fighter (I think touch can be considered more than vague when you actually touch someone). But anyway the fight is kind of over at that stage, I'd give it to the players personally.

HammerJack |

1. Yes. The BBEG needs to deal with the normal difficulties of targeting the fighter, but Sneak Attack is not specially affected. There's nothing ambiguous, there.
2. As we see in the perception chapter of the CRB (page 464), the ability to Seek is contingent on what applicable sense you have to work with. The basic assumption for most creatures is that they only have Sight for a Precise Sense and Hearing For an Imprecise Sense, with only Vague Senses left after that. If your particular BBEG has another Imprecise Sense to use, they'll be able to tell where the PCs are, but not get them better than Hidden. If they only have vague sense to work with, they can't even get to that point, and the PCs will be Undetected.
Senses The ways a creature can use Perception depend on what senses it has. The primary concepts you need to know for understanding senses are precise senses, imprecise senses, and the three states of detection a target can be in: observed, hidden, or undetected. Vision, hearing, and scent are three prominent senses, but they don’t have the same degree of acuity.
Precise senses
Average vision is a precise sense—a sense that can be used to perceive the world in nuanced detail. The only way to target a creature without having drawbacks is to use a precise sense. You can usually detect a creature automatically with a precise sense unless that creature is hiding or obscured by the environment, in which case you can use the Seek basic action to better detect the creature.Imprecise senses
Hearing is an imprecise sense—it cannot detect the full range of detail that a precise sense can. You can usually sense a creature automatically with an imprecise sense, but it has the hidden condition instead of the observed condition. It might be undetected by you if it’s using Stealth or is in an environment that distorts the sense, such as a noisy room in the case of hearing. In those cases, you have to use the Seek basic action to detect the creature. At best, an imprecise sense can be used to make an undetected creature (or one you didn’t even know was there) merely hidden—it can’t make the creature observed.vague senses
A character also has many vague senses—ones that can alert you that something is there but aren’t useful for zeroing in on it to determine exactly what it is. The most useful of these for a typical character is the sense of smell. At best, a vague sense can be used to detect the presence of an unnoticed creature, making it undetected. Even then, the vague sense isn’t sufficient to make the creature hidden or observed. When one creature might detect another, the GM almost always uses the most precise sense available. Pathfinder’s rules assume that a given creature has vision as its only precise sense and hearing as its only imprecise sense. Some characters and creatures, however, have precise or imprecise senses that don’t match this assumption. For instance, a character with poor vision might treat that sense as imprecise, an animal with the scent ability can use its sense of smell as an imprecise sense, and a creature with echolocation or a similar ability can use hearing as a precise sense. Such senses are often given special names and appear as “echolocation (precise),” “scent (imprecise) 30 feet,” or the like.
3 (bonus answer): as for whether the fight is effectively over, it very well might be. I would double check the spell that blinded the BBEG (since it was not specified), as well as their senses. This sort of situation is why the Blindness spell has the Incapacitation trait and tends to not work on bosses above your level, even when cast at your highest spell level, unless they are very unlucky.