Just for fun here's a regex that will work with a single preg_match_all:
'%(?:Filed under:\s*+|\G</a>)[^<>]*+<a[^<>]*+>\K[^<>]*%`
Or, in a more readable format:
'%(?:
      Filed under:   # your sentinel string
    |                
      \G             # NEXT MATCH POSITION
      </a>           # an end tag
  )
  [^<>]*+          # some non-tag stuff     
  <a[^<>]*+>       # an opening tag
  \K               # RESET MATCH START
  [^<>]+           # the tag's contents
%x'
\G matches the position where the next match attempt would start, which is usually the spot where the previous successful match ended (but if the previous match was zero-length, it bumps ahead one more).  That means the regex won't match a substring starting with </a> until after it's matched one starting with Filed under: at at least once.
After the sentinel string or an end tag has been matched, [^<>]*+<a[^<>]*+> consumes everything up to and including the next start tag.  Then \K spoofs the start position so the match (if there is one) appears to start after the <a> tag (it's like a positive lookbehind, but more flexible).  Finally, [^<>]+ matches the tag's contents and brings the match position up to the end tag so \G can match.
But, as I said, this is just for fun.  If you don't have to do the job in one regex, you're better off with a multi-step approach like the one @codaddict used; it's more readable, more flexible, and more maintainable.
\K reference
\G reference
EDIT: Although the references I gave are for the Perl docs, these features are supported by PHP, too--or, more accurately, by the PCRE lib.  I think the Perl docs are a little better, but you can also read about this stuff in the PCRE manual.