When a typical boost converter turns off, there will be a direct current path between the input and output. The output voltage will be one diode voltage drop lower than the input voltage, so it's not really a true shutdown.
Some boost converters emphasize that there is true shutdown function in the datasheet. These types of IC have a switch (MOSFET) between the input and output. When the switch turns off, the output will be disconnected from the input. One example is MAX17222.