Please help me understand how this works:

Julia Brown has a Disrupt that allows the player to sacrifice her and replace her with another Julia Brown or Sleepwalker if she loses a Terror struggle.

This takes place but my opponent plays Power Drain that cancels a response or action, and my opponent plays it to prevent Julia from swapping.

The rules say that a Disrupt is a special kind of Response, so I thought the Power Drain should stop Julia. Is that correct? Does a Disrupt disrupt and Disrupt?

Power Drain cannot target a Disrupt . There are four triggered effects called Action , Response , Forced Response and Disrupt (see page 13 of the LCG rules). Power Drain only targets Actions and Responses .

For contrast, two CCG cards Performance Artist and Court of Yhtill could have cancelled Julia Brown 's Disrupt because they target a character's abilities or any triggered effect, respectively.

So, in answer to your question, the rules definitely allow a player to Disrupt a Disrupt effect, but Power Drain isn't the card to do it with.

cards that can disrupt a dirupt -

aldebaran ascendant

wrack

writhing wall

plus performance artist and court of yhtill.