Frozen Fanfiction : Kristoff's Parents

I have a lot of thoughts/questions about Frozen, but my biggest question is this:

What happened to Kristoff's parents? In the first scene, with the men breaking ice, obviously somebody had brought Kristoff along. His dad or guardian, I don't care, but just somebody who took care of him. But later, adult Kristoff told Ana that the trolls had always taken care of him, he never had parents, etc.

So welcome to my explanation.

Agatha hurled the plate at Bruno. It narrowly whizzed by him, shattering into pieces.

''What do you mean you lost Kristoff?!'' she yelled, preparing another teacup to be thrown.

At this rate, they would have no dishes left.

''Agatha, calm down! I'll find him, I swear! Markus is gathering the men to search right now,'' Bruno said, and, nearing Agatha slowly, stroked her honey-blond hair. Overwhelmed, Agatha buried her head into her husband's shoulder. 

---

''Nothing, Agatha. No pieces of wood from his sleigh, no fur from his reindeer... nothing,'' Bruno sunk into a chair and pushed his hand through his hair. It was obvious Kristoff was dead--three days in the snow and cold, with no food or water...

He should have never taken Kristoff along. He should have watched Kristoff better. Should have, should have, should have.

Agatha's beautiful blue eyes, the same ones Kristoff had, were red with tears. All of the village women had gathered around her, comforting as best they could.

And now his boy, his beautiful rosy cheeked baby boy, was gone forever. 

Should have, should have, should have.