Actually, the term "let them eat 'cake'" refers to the crust that sticks to bread baking pans. Nowadays people use "non stick" or other methods to keep the dough from sticking to the pans. In the 18th century, the baking pans would be coated with "crust" after the loaves were extracted.

The bakers would scrape this "crust" that was referred to as "cake" (because it was the dough that was "caked" on the pans after baking) and distribute it to the poor. It was an important source of carbohydrates for the poor.

The distribution of bread to the "poor" was a common practice (Roman emperors distributed bread to keep the Roman mobs content). The failure of grain ships from Egypt could lead to riots in Rome and overthrow of the Emperor.

So the phrase is referring to allowing the poor to "beg" for "cake" rather than have the government provide them with bread. In effect, it reflects an attempt by a government to cutback an "entitlement" and the population's response to the cutback.