Just use a hard reference: 
use strict;
my $b = '1';
my $a = \$b;

$$a = '2';

print $b;
You must declare $b before referencing it as \$b (I know, I have tested my code), because typing 
my $a = \$b;
my $b = '1';
in this order will autovivify a variable $main::b and then declare a different $b "my" variable.

The reason why your program prints '1' is nearly the same. You can use symbolic references (opr string references as you call it), only to package variables. You cannot use a symbolic reference to a "my" variable. So, in your code, you have two variables: 

my $b
$main::b
That's all !

In reply to Re: can't use string as a SCALAR ref while strict refs by Sweeper
in thread can't use string as a SCALAR ref while strict refs by justinNEE

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