Not exactly right to left, but this code looks for a line that ends with a period, followed by at least one character that is not a period before the end of the line or string. The period and characters that follow it are captured. If the match fails, $suffix is set to a null string. You can specify what you want in relation to the end of the string, but this is not "backwards" or right to left - this is the "rightmost" pattern that matches.

use strict;
use warnings;

foreach my $test ('..', 'file.txt', 'blah.abc.txt')
{
   my ($suffix) = $test =~ /(\.[^.]+)$/;
   $suffix //= '';  #suffix is null string if no match
   print "test=$test  suffix=$suffix\n";
}

__END__
test=..  suffix=
test=file.txt  suffix=.txt
test=blah.abc.txt  suffix=.txt
[download]

There are many modules like: File::Basename.

Update: I guess probably: my ($suffix) = $test =~ /(\.\w+)$/;
Word characters are A-Za-z0-9_. Space and control chars are not allowed.