The indicator in any
fuse indicate system draws minuscule current compared with the normal running current of the device (one hundredth the normal operating current or less would not be uncommon). Essentially, if say the power supply capacitors short-circuit and they blow the fuse then the residual current through the indicator and its current limiting resistor is so low that no additional damage will result. Incidentally, the current limiting resistor and indicator are power rated for short circuit conditions (i.e.: I^2R rating of the indicator and its limiting resistor are such as to maintain the indicator working indefinitely).
extrapickles is correct, and he's right about spring-loaded fuses in old telco gear. Moreover, there are many other systems for indicating faults depending on the type of fault. The issue here is that they don't indicate a fault until one actually occurs—by default they're 'off' until a fault appears.