Actually last will only work on loops. A single block, without any kind of flow control (if, do while, for) counts as a loop that executes only once. So

{
  open my $fh, "<", "some_file" or last;
}
[download]

Will work, and you can make it work with your code by doubling the curly brackets:

if (/VALID/)
{{ # First bracket is for the if, second is for a loop-like block
  open my $fh, "<", "some_file" or last;
}}
[download]

last will never allow you to exit an if-block, because it is often used in constructs such as:

while (<>)
{
  if (/INVALID/)
  {
    last;
  }
}
[download]

Note that it's always possible to name the while loop to provide the name to last and make it clearer what you are leaving.

Edit: completed my last sentence (apparently I forgot what I was saying mid-sentence), and added a condition after the if, so that the code doesn't look so odd.

Edit: BTW, I think that karlgoethebier's version is easier to read.