This is not so special. If you print to a terminal, you might note that this code does work, in the sense that the output appears after two seconds:

alarm 2;
$SIG{ALRM} = \&Finish;
while (1==1){};

sub Finish { print "Timeout reached\n"; }
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After that, the endless loop continues. The only difference is the line feed: STDOUT is typically line buffered if output is to the terminal. So, you just don't see the output. For output to a file or socket, you might want to set $| to a true value.