So, if the display segments is off, then the buffer output pins are low, and you want the display to be off when the processor isn't actively driving the buffer, then the solution is simple.

Just put pull-down resistors on all inputs of the buffer.

When the processor is active, it will win over any pull-down resistors and will drive the buffer high or low.
When the processor is inactive, the pull-down resistors will keep the buffer outputs low.

To reverse the behaviour, you just switch from pull-down to pull-up resistors. Then the buffers will hold the outputs high, when your processor doesn't drive the inputs of the buffer.

You do not really need to have your buffer switch between high, low or tristate, if all you want is for the display to be off when the buffer doesn't get input signals. It's enough that it switches the display segments actively to the "off" state when the inputs are not actively driven. No need to float the signals.