If you have some variable (on the stack) and you left or right bit shift beyond its end what happens?
i.e.
byte x = 1;
x >> N;
<
I think you're confused. x >> y does not actually change x in the first place. It calculates a new value.
As Stephen noted, y must not be negative, and it must be less than "the width of the promoted left operand" (read up on type promotion). But otherwise, bits that shift "off the end" are simply discarded. 1 >> 2 (notice that 2 is not negative, and it is less than the number of bits used to represent 1, which is probably 32 but certainly at least 16) evaluates to 0.