It is getting deleted. If you print the hash after the loop (well, anytime after the delete), you'll notice it only has two keys.

foreach my $id (sort keys %test) {
   delete $test{13};
}

print(scalar keys %test, "\n");  # 2
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Your code is equivalent to

@anon_list = sort keys %test;
foreach my $id (@anon_list) {
   print "$id :: $test{$id}\n";
   delete $test{13};
}
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The problem is that you are deleting the key from %test, but not from the list over which foreach is iterating (@anon_list). That list is built when the loop is entered, before delete is called.

A solution is to check if the key still exists when you get around to visiting it.

foreach my $id (sort keys %test) {
   next if not exist $test{$id};
   print "$id :: $test{$id}\n";
   delete $test{13};
}
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Perhaps you need to elaborate on your problem? The key 13 and its value are being removed. However, why need yo do it in the for loop? Wouldn't it be simpler to remove it up front? Consider:

use warnings;
use strict;

my %test = (11 => "reagen", 26 => "daniel", 13 => "joe");

delete $test{13};
print "$_ :: $test{$_}\n" for sort keys %test;
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which prints:

11 :: reagen
26 :: daniel
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If you need to iterate over the hash entries, manipulate them in some fashion that may depend on other values or keys, then do something with the result you really need two loops. Consider:

use warnings;
use strict;

my %test = (11 => "reagen", 26 => "daniel", 13 => "joe");

for (sort keys %test) {
    delete $test{$_ - 13} if exists $test{$_ - 13};
}

print "$_ :: $test{$_}\n" for sort keys %test;
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Prints:

11 :: reagen
26 :: daniel
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Your question is addressed here: Deleting Hash Entries while Iterating

However, as GrandFather said, perhaps you should tell us more about the problem behind your question; it may be an XY Problem.

HTH,

For more details, see delete. -- this is still useful, of course.