That’s a good question. Here are some examples.
1)You have to wash the dishes in the sink over there. I pity you.
Because this expression is a bit “flowery”, it can be used sarcastically, or humorously. Sometimes, but not always, someone might say, “I pity you,” in order to cause the other person to think again about their problems.
2)You aren’t sleeping well. I feel sorry for you.
3) if you are learning a new language, and you are having trouble understanding native speakers, I sympathize with you! I have the same challenge.