I had a friend who over time I realised was a huge narcissist.
I then had a serious, life-changing traumatic injury and she came to the hospital. She then claimed she was an "empath" and that she could feel my pain so badly that it was affecting her own mental health, and she had to put herself first.
This was her way of letting me know she was about to completely blank me for three months. She told me I had to be more positive "like her". (The irony is that she was the biggest moaner and energy drainer we knew).
The nurse heard everything my "friend" was saying and after "friend" left said "she is no friend to you, she's a nasty piece of work".
"Empath friend" then blanked me for the next few months...but made sure to repeatedly tell everyone around me that she was looking after me and having my kids overnight etc so they didn't need to help me. All classic covert narcissistic behaviour, I later found out.
She really had no idea that she was one huge narcissistic bitch, she genuinely believed she was an "empath" who could magically "feel" people's internal thoughts. And if she thought those thoughts were bad, she would then be a complete bitch to you!
I spoke to a psychologist who said that anyone that claims to be an "empath" is talking utter bullshit and usually they are actually narcissists: "two sides of the same coin" is what many psychologists believe. In my former friend's case she had every symptom of a subset of covert narcissism.
In short, there are people who are sympathetic and nice people. They don't need to claim to be empaths though. And then there are people like her who know there is something wrong with them but don't want to admit to themselves they could be narcissistic, so they self-declare themselves "empaths".