Voltage Regulator IC with Current Overload Indication
You might try looking for a device with a power-good output, rather than a current-limiting output. 

Most simple voltage regulator ICs do not actually limit current directly, although they are advertised with ratings like "1A LDO voltage regulator". Instead, they supply as much current as possible until they overheat and go into thermal shutdown. A regulator like this would turn off its power-good output if it went into thermal shutdown (but you would also lose power).

If you need a precise current limit -- i.e., operation in constant-current mode -- those devices are also available. For example, the Linear LT3050 has both current limiting and an output that indicates when the device is supplying the maximum output current.