The end of your mist line could refer to the cap or plug on the end of your tubing or an auto-drain valve connected to the lowest mist nozzle space in your system. Check your cap or plug as you would any other connection, based on whether it is slip-lock or not. The auto-drain valve has a visible o-ring much like the mist nozzles that can be checked for damage or wear so can be checked in the same way.
An auto-drain valve that leaks when the system is off is doing exactly what it should so there’s no need to worry. Auto-drain valves automatically open when the pressure in a system is reduced to clear the line of water. This can help lengthen the life of your system and cut down on clogged nozzles.
If your auto-drain valve leaks when the line is pressurized, make sure that you are using at least 45PSI or the recommended minimum pressure for your system and that the valve is snug in its connection. If it has been taken apart, it may be missing parts that are needed to keep it closed.