Reminder:

I haven't gotten around to deconstructing those terms yet, but off the top of my head:

This is beta-version-level thought. It isn't surprising that it still has a few rough spots or places where I haven't noticed that I need to explain one thing for another to make sense.

Also, where does fulfilling your function fit into this? Unless you function is just increasing functionality.

Function as I'm intending to talk about it isn't something you fulfill, it's an ability you have: The ability to achieve the goals you're interested in achieving. Those goals vary not just from person to person, but also with time, whether they're achieved or not. Also, people do have more than one goal at any given time.

I have used the word 'function' in the other sense, above, mistakenly. I'll be more careful.

So If I am in extraordinary pain it would never be helpful/ not-harmful for me to kill myself or for you to assist me?

There are two overlapping types of situations that are relevant; if either one of them is true, then it's helpful to assist the person in avoiding/removing the pain. One is that the person has 'avoid pain' as a relevant goal in the given instance, and helping achieve that goal doesn't interfere with other goals that the person considers more important. The other is that the pain is signaling harmful damage to the person's body. There are situations that don't come under either of those umbrellas - certain BDSM practices, where experiencing pain is the goal, for example, or situations where doing certain things evokes pain but not actual (relevant to the individual's goals) harm, and the only way to avoid the pain is to give up on accomplishing more important goals, which is common in certain disabilities and some activities like training for a sport or running a marathon.

Whether suicide would be considered helpful or harmful in a given situation is a function of the goals of the person considering the suicide. If you're in a lot of pain, have an 'avoid pain' goal that's very important, and don't have other strong goals or the pain (or underlying damage causing the pain) makes it impossible for you to achieve your other strong goals, the answer is fairly obvious: It's helpful. If your 'avoid pain' goal is less important, or you have other goals that you consider important and that the pain doesn't prevent you from achieving, or both, it's not so obvious. Another relevant factor is that pain can be adapted to, and new goals that the pain doesn't interfere with can be generated. I leave that kind of judgment call up to the individual, but tend to encourage them to think about adapting, and take the possibility into account before making a decision, mostly because people so often forget to take that into account. (Expected objection: Severe pain can't be adapted to. My response: I know someone who has. The post where she talks about that in particular is eluding me at the moment, but I'll continue looking if you're interested.)

If it weren't illegal or if there was a very low chance of getting caught, I'd be comfortable with helping someone commit suicide, if they'd thought the issue through well, or in some cases where the person would be unable to think it through. I know not everyone thinks about this in the same way that I do: 'If they've thought the issue through well' doesn't mean 'if they've fulfilled the criteria for me to consider the suicide non-harmful'. Inflicting my way of thinking on others has the potential to be harmful to them, so I don't.

Finally, I guess you're comfortable with the fact that the function of different things is determined in totally different ways? Some things get to determine their own function while other things have people determine it for them?

There's an underlying concept there that I failed to make clear. When it comes to accomplishing goals, it works best to consider an individual plus their possessions (including abstract things like knowledge or reputation or, to a degree, relationships) as a single unit. One goal of the unit 'me and my stuff' is to maintain a piece of territory that's safe and comfortable to myself and guests. My couch is functional (able to accomplish the goal) in that capacity, specifically regarding the subgoal of 'have comfortable places available for sitting'. My hands are similarly functional in that capacity, though obviously for different subgoals: I use them to manipulate other tools for cleaning and other maintenance tasks and to type the programs that I trade for the money I spend on rent, for example.

(This is based on the most coherent definition of 'ownership' that I've been able to come up with, and I'm aware that the definition is unusual; discussion is welcome.)

As far as I can tell, people determine the function of tools and this notion that people determine their own function, while true in a sense, is just Aristotelian natural law theory rearing its ugly head. It used to be that we have purposes because God created us and instilled us in one. But if there is no God it seems that the right response is to conclude that purpose, as it applied to humans, was a category error, not that we decide our own purpose.

I think I've already made it clear in this comment that this isn't the concept I'm working with. The closest I come to this concept is the observation that people (and animals, and possibly AI) have goals, and since those goals are changeable and tend to be temporary (with the possible exception of AIs' goals), they really are something entirely different. I also don't believe that there's any moral or objective correctness or incorrectness in the act of achieving, failing at, or discarding a goal.