There is no logical reason why nested calls of the same function (i.e. recursions) should act differently to nested calls of different functions.

see updated code, especially the second paragraph contrasting the bug.

UPDATE:

to be sure to avoid any side effects from eval within the debugger here a standalone file for testing:

use warnings;
use strict;
use 5.10.0;
 
my $x;
 
sub delchar { $x =~ s/(\w)// ?  $1 . delchar() . $1  : "x" }
 
$x='abc';
say delchar();                            #  => "cccxccc"
 
 
  
sub del1 { $x =~ s/(\w)// ? $1 . del2() . $1 : "x"  } 
sub del2 { $x =~ s/(\w)// ? $1 . del3() . $1 : "x"  } 
sub del3 { $x =~ s/(\w)// ? $1 . del4() . $1 : "x"  } 
sub del4 { $x =~ s/(\w)// ? $1 . del5() . $1 : "x"  } 
 
$x='abc';
say del1();                              # => "abcxcba"
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UPDATE:

Best practice is to copy captures like $1 ASAP! (not only in recursions)

  DB<105> sub delchar { my $m; $m = $1 if $x =~ s/(\w)//;  $m ?  $m . 
+delchar() . $m : "-"  }
 => 0
 
  DB<106> $x='abc'; delchar()
 => "abc-cba"
 
  DB<107> sub delchar { local $m; $m = $1 if $x =~ s/(\w)//;  $m ?  $m
+ . delchar() . $m : "-"  }
 => 0
 
  DB<108> $x='abc'; delchar()
 => "abc-cba"
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