That will loop through the file, but then it will continue to loop forever with 'AFTERFILE' in $_. So if you're going to do that, you'd have to do it as

while (defined($_ = <INHANDLE>) || ($_ = "AFTERFILE")){
    stuff;
    last if $_ eq "AFTERFILE";
}
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and of course, if the file actually contains AFTERFILE, you're in trouble.

So if you don't mind undef as your special after loop value, it's probably easiest to do something like

LOOP: {
    $_ = <>;
    stuff;
    redo LOOP if defined;
}
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