I tried to replicate (as simply as possible) the situation you described, which I think would go like this (using "find" as "program C" -- I'm running linux too):

#!/usr/bin/perl
# PROGRAM "A"

my $pid = fork();

if ( $pid ) { while (1) {sleep 3} }
else { exec( "/tmp/junk.perl" )   }

__END__

#!/usr/bin/perl
# PROGRAM "B"

system( "find / -ls > /tmp/junk.find 2>&1" ); # this takes a while

__END__
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The only way I could make it so that "program C" ("find") kept running after ctl-C stopped "A" was if I added "&" in the system call to run C in the background:

system( "find / -ls > /tmp/junk.find 2>&1 &" );
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In this case, of course, the "B" process becomes defunct very soon (it exits after launching "C" in the background), so no amount of signal handling in perl would stop C, unless I took steps to make C's pid available to A, and kill it from there.

You didn't say much about the system call issued in B to launch C; does it background C? Are you sure B is still running when you halt A?

Would it be practical for B to open( C, "process_C |"); or something like that? This way, when B closes the file handle, C is terminated.