Unless you tell us more about your infrastructure, the answer is likely to be "no".

As an approach, I could see to launch the FCGI server part in one thread and launch some more worker threads separately.

You should be advised that mixing threads and signals is highly OS+clib specific and most likely does not do what you want. Maybe only your main thread will receive signals, but maybe all threads will receive signals, or just a random set.

I use following code:

#!/usr/bin/env perl

use v5.16.3;
use threads (exit => 'threads_only');
use threads::shared;
use IO::Select();
use FCGI;

my $listen = ':5000';

my $socket = FCGI::OpenSocket($listen, 100);

$SIG{INT} = sub {
    map { $_->kill('TERM') } threads->list(threads::all);
};

threads->create(\&thread, $socket);
threads->create(\&thread, $socket);
threads->create(\&thread, $socket);

while (threads->list(threads::all)) { sleep 1 }    #wait until all thr
+eads finished

sub thread {
    my $socket = shift;

    $SIG{TERM} = sub {
        threads->detach;
        threads->exit;
    };

    my $env = {};
    my $req = FCGI::Request(\*STDIN, \*STDOUT, \*STDERR, $env, $socket
+, 1);
    my $sel = IO::Select->new($socket);
    while (1) {
        if ($sel->can_read(1) && $req->Accept() >= 0) {
            print "200\x0D\x0A";
            print "Content-Type: text/plain\x0D\x0A";
            print "\x0D\x0A";
            print threads->tid . "\x0D\x0A";
            $req->Finish;
        }
    }

    return;
}
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Problem with blocking $req->Accept seems to be solved. As you can see, I use IO::Select to make non-blocking check if socket ready to accept connection.

Non-blocking accept is needed to give process possibility to process received signals, because signals in threads is not OS level, but perl emulated and don't break system calls.

$sel->can_read(1) return true in all threads, when new connection is ready to be accepted.

I don't know, can system call $req->Accept() return positive value for several callers simultaneously?

If it can - this code need to be modified.

Now, in my tests, it return 0+int to first caller, who really accept connection, and negative value for all others.

This solution is not work under MSWin, because:

select (the underlying system call used by IO::Select) only works for 
+sockets in Windows.
[download]

and FCGI.pm seems use pipe or something else in windows. Please, help resolve this problem.