It means to foresee or be prepared for an event, typically an unpleasant one. Or maybe they didn’t, so they didn’t see that coming.

The meaning comes from the days when wearing a cap or hat was considered part of a man’s wardrobe when out of the house.

To show respect, you would take your hat off and hold it in your hand, especially when the person you are talking to is more senior in rank or holds a position of respect (the bank manager).

You can't have your cake and eat it

Overview
The aroma of flavoured sponge cake is modified following storage in a glass container or paper and plastic packaging, say French scientists, who combined solid-phase microextraction with GC-olfactometry to compare the aroma barrier properties of the packaging materials.

I have long maintained that a good chemist should also be a good cook. Chemical recipes tend to be quite precise about the quantities of reagents to add and to drift from the exact formula can have dire consequences on the yield of the final product. Conversely, you can get away with murder when you bake a cake. How much is a cup of sugar or a pinch of salt? Follow a reasonable approximation of the recipe and you can still produce a masterpiece.
 
[Wiley Analytical Science | 01.04.07 | LINK]