You're problem has nothing to do with system. The problem is in these lines.

my $dir = @dirs_sunflarebeam;
#print "$dirs\n";
system("getfacl", "$dir");
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$dir contains the count of the items in @dirs_sunflarebeam, not the first item. The call to getfacl can't find a file named 1. You probably meant my $dir = $dirs_sunflare_beam[0];

One minor nit: You don't need the quotes around $dir in the last statement. They really have no effect.

Update: formatting correction.