Unfortunately, that gives a warning.

I note that:

  use strict ; use warnings ;

  our $inner = "SET" ;

  sub inner {
    my ($s) = @_ ;
    print "$s  outermost inner \$inner=$inner\n" ;
  } ;

  print "outermost start\n" ;
  inner('') ;
  buddy('') ;
  wrapper('') ;
  buddy('') ;
  print "outermost end\n" ;

  sub wrapper {
    my ($s) = @_ ;

    print "$s  wrapper entered\n" ;
    inner($s.'  ') ;

    local *inner ### ; print "$s  *** separate local\n" ; *inner
      = sub {
          my ($s) = @_ ;
          $inner ||= "NOT SET" ;
          print "$s  innermost inner $inner\n" ;
        } ;
    inner($s.'  ') ;

    buddy($s.'  ') ;
    print "$s  wrapper exit\n" ;
  } ;

  sub buddy {
    my ($s) = @_ ;
    print "$s  buddy entered\n" ;
    inner($s.'  ') ;
    print "$s  buddy exit\n" ;
  } ;
[download]

gives:

outermost start
  outermost inner $inner=SET
  buddy entered
    outermost inner $inner=SET
  buddy exit
  wrapper entered
    outermost inner $inner=SET
Subroutine main::inner redefined at zz.pl line 29.
    innermost inner SET
    buddy entered
      innermost inner SET
    buddy exit
  wrapper exit
  buddy entered
    outermost inner $inner=SET
  buddy exit
outermost end

showing the same warning. Also the value of $inner is unaffected by the local -- which may or may not be a surprise.

But if you remove the ### in the code above, to make that line:

    local *inner ; print "$s  *** separate local\n" ; *inner
[download]

that gives:

outermost start
  outermost inner $inner=SET
  buddy entered
    outermost inner $inner=SET
  buddy exit
  wrapper entered
    outermost inner $inner=SET
  *** separate local
    innermost inner NOT SET
    buddy entered
      innermost inner NOT SET
    buddy exit
  wrapper exit
  buddy entered
    outermost inner $inner=SET
  buddy exit
outermost end

NB: using the stand alone local *inner is undefining all parts of *inner.

I guess that the '=' is doing special things to assign the rhs to the right part of the lhs GLOB, so this is not a run of the mill assignment. Could this be why the presence of the initialiser appears to change the effect of local on a GLOB ?

You will recall that in another thread Setting signal handlers considered unsafe? it was established that  local $SIG{ALRM} = ... that the local sets the lhs undef before the assignment takes place. Which this isn't consistent with !