s:$:__:
s:...:& :g
s: _*$::
Try it online!
It gets a bit tricky regarding the empty string input, since sed has no meaning of a falsy value. So to deal with this, I provide you with two possible interpretations of the rules to validate my submission:
A. You essentially provide nothing as input, not even a trailing newline (as it is the case with all the examples, including that 6 Mb file).
Usage:
echo -n ""|sed -f script
Output: nothing is printed, because sed doesn't even run the script without input.
B. One could consider as falsy value for sed to be an unique string, i.e., returned only when the input is an empty string.
Usage:
echo ""|sed -f script
Output:
__
I prefer the first interpretation so much more, as I believe it to be the closest to the intended rule, but the last one helps if you run the script using that TIO link.