depends on the problem...
Is some cases, the ECU will go to normal operation if the faulty device/sensor/condition has been resolved. The fault code remains to let the technician know what was happening. If the MIL indicator is on, it may remain on until the code is cleared.
There are other cases where the code has to be cleared to reset learned values and get things back on target.
Now that we talked in generalities, care to share some specifics?