Diva Plavalaguna did not mean to survive the experience.
Here's the exerpt from the script, in the scene where Diva arrives, walks past Leeloo and touches her:
... The Diva reaches out and strokes Leeloo's face, without touching her. The Diva removes her hand making a sound of crackling electricity, then passes on. Leeloo is groggy.
The Diva's ASSISTANT comes up to her.
Please forgive this little incident. She wants you to know that she senses great powers in
you... in the service of a noble cause...
She will give you what you have come to get, but she wants to sing first...
One last time...
That last details implies that Diva does not expect to survive. Whether it is because she intends to die during extraction as there's no other choice; OR because she's prescient and knows what will happen is not clear; but a latter detail from a script hints at the latter option:
She [Diva] falls from the stage into Korben's arms. He lowers her to the floor.
Korben ignores the panic all around and wraps her in his dinner jacket,
trying to stop the blue blood spurting from her wounds.
(to the Diva)
I was sent by the government to help you.
Don't worry. This is my fate...
How was the concert?
 Presumably, the name - which means "blue lagoon" in Croatian - is a reference to Milla Jovovich's first film "Return to the Blue Lagoon").