Power supply switch-off characteristics
Power down (and up) sequencing can be a problem in some circuits. For example an MCU or FPGA might have 5 V tolerant pins, but only when the chip is powered, or a circuit might get powered through a device's input protection diode which can only handle a few milliamps. Some chips have multiple supply rails that have to go up and down in a particular sequence to avoid damage (eg. the Intel 8080 CPU).

A power supply can be designed in such a way that some voltages are guaranteed to come up and go down before/after others, or all at the 'same' time. This might be worthwhile in a dedicated supply, but could make it more complicated and less flexible (= more expensive) than a 'generic' supply. 

Most supplies are designed to hold their outputs up as long as practicable in a 'brownout', and the time they hold up for depends on the current drawn. It is then up to the system designer to make sure the devices being powered can handle it, or add circuitry to produce the required sequencing. 

You could 'open' the supply using a power MOSFET controlled by a voltage comparator that turns it off when a brownout is detected. However this still might not be sufficient if there is a lot of 'bulk' capacitance further on in the circuit. The power on sequence may also need to be considered, which could make the control circuit quite complex.    

Other solutions include powering everything from the same voltage, adding more bulk capacitance to parts of the circuit that have to stay powered up longer, disabling regulators when brownout is detected, protecting inputs with series resistors to limit current (possibly combined with external protection diodes) optocouplers, level shifters etc. In some circuits a relay may be the best option!