Answer:
Soft hairy from door to door. I am the pet that always stays on the floor.
I store fire-breathing animals.
You heard me before and then again. Afterward I die until you call me again.
You throw me away, I find my way back. Traditionally, I'm wooden with an arch in my back. What am I?
If you lose me, you may cause people around you to lose me too. What am I?
The answer I give is yes, but what I mean is no. What was the question?