{ 
    package Undef; 
    sub TIESCALAR{ bless \pop, 'Undef';} 
    sub STORE{ $$_[0] = $_[1]; } 
    sub FETCH{ defined $$_[0] ? $$_[0] : 0 } 
};

tie $x, 'Undef';

$x = 0; print "'$x'";
'0'

$x = ''; print "'$x'";
''

$x = undef; print "'$x'";
'0'