I recommend against your plan -- it is unduly complex -- but it is possible using operator overloading.

use strict; 
use warnings;


package Character;

use AutoExecute;

sub new {
   my ($class) = @_;
   return bless({
      poisoned => 0,
   }, $class); 
}

sub poisoned {
   my ($self) = @_;
   return auto_execute {
      my ($poisoned) = @_;
      $self->{poisoned} = $poisoned if @_;
      return $self->{poisoned};
   };
}


package main;

my $char = Character->new();
my $poisoned = $char->poisoned;
print($poisoned, "\n");  # 0
$poisoned->(1);
print($poisoned, "\n");  # 1
$poisoned->(0);
print($poisoned, "\n");  # 0
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AutoExecute.pm: (Could probably use a better name)

package AutoExecute;

BEGIN {
   our @EXPORT = qw( auto_execute );
   *import = \&Exporter::import;
}

use overload
   '""'  => \&stringify,
   '&{}' => \&code_ref,
;

sub auto_execute(&) {
   my ($sub) = @_;
   return bless(\$sub); 
}

sub new {
   my ($class, $sub) = @_;
   return bless(\$sub, $class); 
}

sub stringify {
   my ($self) = @_;
   my $sub = $$self;
   return $sub->();
}

sub code_ref {
   my ($self) = @_;
   my $sub = $$self;
   return $sub;
}

1;
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But all of the above would be much faster and just as neat if written as follows:

use strict; 
use warnings;


package Character;

sub new {
   my ($class) = @_;
   return bless({
      poisoned => 0,
   }, $class); 
}

sub poisoned {
   my ($self, $poisoned) = @_;
   $self->{poisoned} = $poisoned if @_ >= 2;
   return $self->{poisoned};
}


package main;

my $char = Character->new();
print($char->poisoned, "\n");  # 0
$char->poisoned(1);
print($char->poisoned, "\n");  # 1
$char->poisoned(0);
print($char->poisoned, "\n");  # 0
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