Fe feels what someone feels right now, whatever it actually is. it may not be able to predict what the very same person will feel if his situation changes, but it can likely predict how that specific individual would react to a having a specific feeling. this is because introverted perception creates a virtual subject that has a specific character (modeled after the observed person) that would feel about a given thing in a given way, and it can tell how the very same character would react if that specific emotional logic is triggered in a certain way.
Fi feels what it (itself) would feel like in a fictional circumstance, so Fi can be empathic about poorly told stories about what happened to someone (Fe cant do that) (stories that do not include information about how someone felt about it), but its personal, meaning it only works reliably if the empath and "target" are similar in what the fictional situation means to them. that's like "do unto others as you would want to be treated". of course, a deep personality can chose a part of their own subject, that is similar to the target, and feel about the fictional situation with that specific part of themselves. this selection process is what introversion does in the realm of the introverted function. Fi can also assume that one emotional logic is likely paired with another emotional logic in the same individual. that's why Fi can tell how a fictional situation would likely trigger a specific emotional logic that has not yet been observed in the individual.
this selection of a specific part of ones own subject, which matches the observed individual is also what introversion does in the realm of intuition or sensing. that's why introverted perception is all about sharing views (knowing what one can understand, how he interprets, what reaction his interpretation will likely activate), which is not empathy but a cool profiling, and what i said above about how Fe can predict a reaction to an emotion, the emotion being the product of an interpretation, is related to and dependent on that. usually Fe is combined with introverted perception. if it is not, like in the case of Ti-dom with Fe shadow, that profiling thing does not work very well.
none of that is mere sympathy. sympathy meaning that you recognize someone as buddy if he coincidentally feels, thinks or appreciates (taste=sensing) what you happen to like to begin with. sympathy does not require any amount of introversion in any function, because it does not require selection or compilation of a specific subjectivity that matches the person you are dealing with.
a bit disorderly this text ... but meh