File handles can go out of scope, if you use localized typeglobs.

{
    local *FH;
    open FH, ">output.txt" or die "Can't write to file: $!";
    print FH "Anything...\n";
    printf STDERR "fileno for FH: %d\n", fileno(FH);
}
# ...
open FH2, ">output2.txt" or die "Can't write to file: $!";
printf STDERR "fileno for FH2: %d\n", fileno(FH2);
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The file handle will be closed when the block is exited. It is extremely likely that you'll see the same value for fileno() for both handles... (for this as a script, I expect to see the value 3) indicating that the first one was released, thus, the handle got closed.