Maybe check if $gz is an empty string and don't try to call gunzip() in that case?

I also can't reproduce your problem. eval catches the error message correctly for me with your code (amended below to show that):

use 5.012;
use warnings;
use Gzip::Faster;
my $gz="";
my $data;
eval {$data=gunzip($gz)};
if($@) {
    say qq(error: $@)
};
say "Done"
[download]

This gives me the output:

Attempt to uncompress empty string at ...
Done
[download]

Most likely the code you post is not the code you run.