This C-style for:

1 =~ /1/; 
for (my $i = 3; $i =~ /[34]/; $i++) {
    print $&; 
}
print $&;
[download]

says 341, not 344. Isn't it because of beyond-body, outer-implied-braceless scope, which is same as in similar while loop?

Or did you mean something else, by "per-pass" (is it same as "per-loop") scope? The confusing part is why $& in OP (but not localized $x in hv's code) preserves its value between iterations.

And further (maybe unrelated; sorry, have just seen it, can't un-see):

1 =~ /1/; 
for ((my $i = 3) =~ /./; $i =~ /[34]/; $i++) {
    print $&; 
}
print $&;
[download]

says 343. Again, sorry if it's waste of time, these are (questionably) good in idle golf etc., seem not have bothered busy people in 30+ (?) years.