Word for someone who is too empathetic (possible antonym of narcissism)

I am looking for a word describing someone who has an "unhealthy" amount of empathy to the point where it may be detrimental to their well-being.

For example, on the other side of the scale, one may have confidence in a healthy way. Such people may proud of themselves, expressive, independent, and not overly concerned with how people view them. Taken to the extreme, this might become arrogance or narcissism ("unhealthy confidence").

At the other end of the scale, someone might very empathetic and humble. They may care deeply about the feelings of others, able to sacrifice their immediate needs, and not overly concerned with expressing themselves outwardly. Taken to the extreme, they may place others before them so much that they end up hurting themselves or fail to advocate for themselves. Is there a word for this kind of "unhealthy empathy"?

(Note that confidence and humility are not necessarily mutually exclusive... I think what complicated this question is that I am mixing too many related, but not the same, ideas together).

You might say that this person is empathetic to a fault:

(of someone who displays a particular commendable quality) to an extent verging on excess.

"you're kind, caring and generous to a fault"

synonyms: excessively, unduly, immoderately, overly, needlessly

"Katherine is very giving, sometimes to a fault"

Generally, over-empathetic people are referred to as bleeding hearts

A person who shows extravagant sympathy, especially for an object of alleged persecution

I do not know of any single word equivalent; sentimental and sympathizer are both words you might consider modifying with appropriate adjectives, though.