Hm... I don't comment what you said, as I am not sure whether I actually have understood what you said as it meant to be. Any way, try those two pieces, and hope they mean something to you (no harm, food for thought :-):

use strict;
use warnings;

my $s = "1..11";
while (my $line = <DATA>) {
    print "line = $line";
    print for (1..10 or $s);
    print "\n";
}

__DATA__
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
[download]

And this:

use strict;
use warnings;

my $s = "1..11";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";
<DATA>;
print for (1..10 or $s);
print "\n";

__DATA__
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
[download]

To explain why the two differ (where the second is just an unwrapped loop, pretty much otherwise equivalent to the first):

Each flipflop operator has its own independent hidden state variable in the pad. It acts like a my $flipflopstate at the top of the enclosing sub or file, only a different variable for each flipflop in the sub/file.

Thus, in your second example, the first 1..10 gets set true (because $. is 1) but none of the later ones are (because they never pass the beginning check for $.==1).

In the first example, the flipflop returns true 10 times because it meets the $.==1 check the first time and doesn't meet the $.==10 check until the 10th time.

Note that because the hidden state acts like sub-scoped lexical, a recursive call to the sub will start with a fresh state, and ditto multiple threads in the same sub.