The cart card says specifically- "Save up to 2 valuable crystals in your chest to be sold at the end of another day."
Does it act as safe storage for the entire game? The group I play with says that no players can steal from the chest- and keep jewels there the entire game. I want to know if that is the intended use for the cart card.
The crystals stored in the chest are save.
Imagine that the chest is in your "home", not in the mine.
You can leave the crystals there as long as you like, and sell them whenever you like.