The problem is an extra set of braces you are using in the second bit of code there. You have a nested bare block inside the foreach, the next breaks out of it, NOT the foreach.

use strict;
my @list = qw(0 1 2 3 4 5);
foreach (@list){ #opens up the foreach block . . .
  {              #opens up a new block . . .
    next if $_ == 0; #breaks out of enclosing block
  }                  #meaning it breaks to here.
  print $_, " ";     #so '0' get's printed anyway
}                    #ends the foreach
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Be careful about these extra blocks by using labels and explicitly breaking with them. Labels are goood practice for complicated loop structures anyway, for clarity's sake.

Cheers,
Erik