I think what you really want to know is when the sub starts, and when it finishes, regardless of whether it finishes because it falls off the end of the sub, returns, or dies. Serendipitously, those are exactly the times when a sub-scoped lexical variable goes out of scope. If you create an object when the sub starts and hold it in a lexical variable, you can print the Entering message in its constructor, and the Exiting message in its destructor. Here's a short example:

#!/usr/bin/perl

use warnings;
use strict;
package SubLog;

sub new
{
  my $class = shift;
  my $self = {
    name => (caller(1))[3],
  };
  warn "ENTERING SUB: $self->{name}\n";
  bless $self, $class;
}

sub DESTROY 
{
  my $self = shift;
  warn "EXITED SUB: $self->{name}\n";
}
package main;

sub blahblah
{
  my $sublog = SubLog->new;
  return 5;
}

sub blahsub
{
  my $sublog = SubLog->new;
  blahblah();
  return 3;
}

blahsub();
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