Check $! to see if any error occured. See perldoc perlvar.

Also, this isn't shell so you shouldn't be putting the variable name in quotes if you're only using it by itself. -s $filename is fine. If the variable you were trying to pass to -s were a filehandle glob reference, the quotes would actually break your code entirely by turning the reference into a useless string representation of its address.

my $size = -s $filename;
die "Couldn't stat $filename: $!" if not defined $size;
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Makeshifts last the longest.