Verified answer

I do apologize- I was in this show, but it's been a couple of years, so I'm trying to piece together as best as possible.

Julie and Jean aren't related actually. He is a servant on her estate, and her dreams forshadow what is to come, as do his. Once they have betrayed their class code, by sleeping together before marriage (and outside of their classes), they soon realize that they have no choice but to flee, or die. When Jean kills Julie's bird at the end, she realizes that she has only the choice to flee before her father returns, becoming her servant's mistress, or to kill herself, since she has disgraced her name, and her status.

I know it's a difficult play to read, but try to make it through. Seriously, you'll find all you need if you just read it. Also try looking up sparknotes on Miss Julie- they may have it broken down.