If you have a gold foil print crossing from one to another side of the box (a simple skincare packaging cardboard box -like in the example), is there any danger of the foil getting damaged when the cardboard is folded and bended on those edges?
Because the foil overlay is to be considered a distinct and separate layer to the packaging, it will have semi-independent characteristics of note.
The typical method of addressing this bending effect/problem is that the folded sections are embossed at the point of the bend. The foil has to "travel" a greater distance to cross the valley created.
Along with creating an easier folding location, the valley/embossing pre-stresses the foil and shortens the distance once the part is bent.
The top drawing shows a depressed/embossed section (not to scale) with a top dotted line representing the foil if it was not embossed. The length of the top dotted line is much less than the total of the two angled lines below it.
The bottom drawing shows that the panels can be folded to 90° while maintaining the same dimensions of the foil that crosses the valley, so to speak.
If you are having a product manufactured to your specifications, the vendor should have this knowledge and should have equipment designed to perform such actions.
Once the product is constructed, the edges will indeed be subject to wear and damage, but there's little that can be done from a design aspect to mitigate this aspect.