It depends on the person. Under no circumstances should anyone eat less than their BMR; however, recommendations are that men eat no less than 1500 calories a day, women eat no less than 1200.
Just as an example, if a woman's TDEE (number of calories to maintain her current weight) was 2400 and her BMR was 1200, then she could "easily" have a deficit of 1000 calories a day, which would bring her to 1400. However, "easily" is a matter of very strict nutrition, and can be difficult to maintain.
Goldie, those are already pretty low amounts. Even if you fix the calorie deficit you are aiming for (say, 500 kcal/day), it is healthier to eat 1500 kcal and have a TDEE of 2000 kcal than to eat 1200 and have TDEE = 1700. In other words, "your body works best at a high calorie turnover". The difference between the two scenarios is, of course, the amount of exercise you do.
Aiming for the higher value has several advantages. For me the most important are these two:
- Doing the cardio has the obvious advantages of strengthening your heart, improving your lung capacity, etc etc; I won't go into details here. I will simply note that lung capacity (specifically, VO2 max) is a better predictor of mortality than being overweight or obese. So if you are doing this for health, a calorie deficit is not the ultimate solution.
- If you eat more calories, it is less likely that you will have deficits of essential nutrients such as vitamins and essential fatty acids. It is also easier to eat a more varied diet because you are not counting calories as strictly.
In a recent study I read there is a pretty significant decrease in mortality with the TDEE increase. Specifically, they recommend a minimum of 1500 kcal per week spent on exercise for women, and 2000 kcal/week for men. I did the math and it amounts to around 4 hours per week of jogging at a reasonably fast pace. It also adds up to about 2000-2300 kcal TDEE for women, and 2500-2800 kcal TDEE for men.
In other words: if you are aiming to be healthy (which will also make you more attractive, if that's your goal), it's best to up your cardio than to lower your eating.