Voltage Rating: If a capacitor cannot handle the voltage applied to it, it may fail prematurely. This is often due to selecting a capacitor with a voltage rating too close to the operating voltage. Current Capacity: Similarly, capacitors have a maximum current capacity. Exceeding this capacity can lead to overheating and failure.
Operating a high voltage capacitor at lower dc voltage cause some low continuous current to flow through the capacitor, thus rendering the capacitor not behaving ideally as a capacitor. The voltage rating of the capacitor is the point at which the dielectric & insulation between the two plates starts to break down and fails.
A leaky capacitor has the effect of a large rated capacitor that leaks and keeps the circuit from working properly. In most cases, you can over rate a capacitor and get away with it. If you double the voltage value of the capacitor but keep the supply voltage low you might want to also double the Farad value.
You tend to find more like the opposite. A high voltage capacitor will have it's capacitance rated at low voltage meaning when operated close to it's rated voltage the capacitance will be much lower. This is why the different MLCC capacitor dielectric types exist, they guarantee a certain capacitance vs voltage characteristic (amongst other things)
This characteristic is assumed to be due to the deterioration of the dielectric oxide layer at high temperatures, which reduces the insulation of the capacitor, and applying a DC voltage to a capacitor in this state causes the leakage current to increase. How to do, what to do?
Rule of thumb round here is that caps rated for 2x the working voltage is a good (reliable) part. You tend to find more like the opposite. A high voltage capacitor will have it's capacitance rated at low voltage meaning when operated close to it's rated voltage the capacitance will be much lower.