At the end Elsa couldn't even get out of bed. That's where Olaf found her.
"Elsa?" He walked to the edge of the bed and touched her outstretched hand.
"I'm sorry Olaf, I can't keep you cold any more."
"That's alright, this one time, I wanna be warm."
And they faded from existence together...
Anna wandered the halls in black clothes, until she reached her sister's door.
"Elsa, you're not in there,
people are crying now you've gone,
they say let go now and I'm trying to,
I'm letting go!
We only had each other, for so long,
What am I gonna do?!
We'll never build that snowman."
She sat against the door and on the other side, a near invisible figure leaned her head against the door. When Anna's children found her hours later they took her back to her room. And Elsa's ghost followed them.