kosun, as gellyfish's quote from perlvar says, you might be able to control things with a 'goto':

$SIG{'__DIE__'} =
    sub {
        if ($_[0] =~ /matched error text/) {
            print('Warning - continuing after error: ', $_[0]);
            goto &foo;
        } else {
            print($_[0]);
        }
    };

sub foo
{
    print("Continuing in 'foo'...\n");

    # Do more work...
}
[download]

Your app will then exit when 'foo' returns.