Where the rule comes from
One pound of stored body fat holds approximately 3,500 kilocalories. Divide 3,500 by 7 days and you get 500 -- the origin of the popular "500 kcal/day deficit equals 1 lb/week" heuristic.
The hidden assumption
The rule assumes your Total Daily Energy Expenditure (TDEE) stays constant throughout your diet. It does not. As your weight drops, so does your TDEE -- meaning a "500-calorie deficit" calculated on day one is smaller in practice by week ten, unless you deliberately recalculate and re-cut.
A concrete example
Someone starting at 2,650 kcal TDEE eating 2,150 kcal/day begins with a genuine 500-kcal deficit. By the time they've lost 20-25 lb, their TDEE may have fallen closer to 2,450 kcal -- shrinking the same 2,150 kcal intake down to roughly a 300-kcal deficit, and slowing weight loss by nearly half without any change in behavior.
What a more accurate model looks like
Tools that recalculate TDEE at intervals -- or that simulate the recalculation continuously across a full timeline, as a Monte Carlo model can -- consistently show slower back-half progress than the static 3,500-calorie rule predicts, which matches what most dieters report anecdotally.