The OP doesn't understand Fi & probably thinks it's only about understanding how you feel & then judging things by your personal ideals according to what you need (which people reduce to "self-absorbed" or worse "selfishness").
So let's get this out of the way first:
Empathy - the intellectual identification with or vicarious experiencing of the feelings, thoughts, or attitudes of another.
So empathy is not necessarily becoming personally affected with the same emotion the other person is feeling, but it can be an intellectual identification, or a deep understanding of what the emotion/feeling is & why it exists in that person.
How does this work in a FiNe type (and probably similarly in a NeFi type)?
As a Fi type, you yourself are an upclose case study of the inner nature of people. If you were to dissect a frog & study its insides, then you may have a general idea of what the insides of a frog look like, right? The Fi type does a thorough dissection of themselves - their feelings, their emotions, their needs, etc, and then goes deeper with it, past the surface implications, to identify the fundamental human need at core that goes beyond their own personal preferences. In this way, they understand how people work & can identify why they are responding a certain way emotionally.
When it comes to empathy, it's a matter of "I know what it is to feel pain, so I can recognize pain in others & know that it is bad". I can tell you that I have spent a lot of time exploring emotions & feelings in the manner of "if this happened, how would I feel?" and also via art, music, literature, etc. This gives me a lot of hypothesis to work from, where my experience may be limited. I have a sort of prototype of human feeling built up in my head.
So the Fi+Ne type in particular does not have to personally experience something to understand how it can affect someone, nor do they themselves have to have the same response (because knowing that people are affected very differently is an edge Fi has over Fe, which tends to see feelings as objective & almost inevitably shared; this awareness may come from seeing the huge difference in yourself from others at a young age). I think [MENTION=8074]Seymour[/MENTION] once described this process as "simulating someone else in your head", by grasping their essence as a person & considering how you would feel if you were them in their situation, NOT if you were you in their situation. Is Ne involved in this? Most likely, because it involves taking on different external perspectives to understand a relationship (in this case, the relationship between a person's feelings/emotions & whatever affected them) & grasping the "big picture" of a person so as to imagine yourself as them very vividly. You are extrapolating foreign feelings from known feelings & known information. "Extrapolating" is a key word for me in this process; I think it really hits on the manner in which a Fi+Ne type empathizes. I personally see xxFPs as MUCH better at understanding foreign feelings than xxFJs, who seem more focused on what is a "normal" response, based on their observations & other external criteria. If someone is sad, they seem able to empathize with the emotion because the recognize & feel their sadness, but they may not always see why someone feels that way, not if they don't see the emotion as being the normal response. This is because emotions signal value, and a value that is not externally sourced is not necessarily valid to the Fe type.
The xxFP may be less prone to being emotionally affected themselves when they empathize though (but sometimes we can be, if it really hits on an ideal, whether meeting it or violating it). I agree with [MENTION=5684]Elfboy[/MENTION] that it feels like you're making sense of something, which seems weird to people who see emotions as not having any sort of structure (to a Fi type, they do). I admit I sometimes think of these instances as solving "emotional puzzles", which sounds detached, but I have a strong moral pull to do so, which is not detached at all.
I'm making it sound really technical just to explain it clearly, but it's not really experienced that way. There's a lot of sudden realizations & connections & grasping of intangible essences (very Ne) & then making sense of it based on that Fi insight into people.
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Oh yeah, I have to echo that I tend to empathize with fictional characters easily & can be deeply disturbed by violence in movies too. My ESFP sister doesn't get this either...because it's "not real". I think it's an NF thing, where you focus on an idea & glean meaning from it, and that often means an emotional response.
