1) you are reading fixed length records and retrieve a record containing all '0's, 2) you have set $/ to a string of one or more '0's, or 3) the last line of a file you are reading must contain a string of one or more '0's and not be terminated with $/.

Not to be too pedantic, but you keep saying "a string of one or more '0's", when it is only a string of a single zero that evaluates as false.