As doug748 shows in this picture you should be left with simply the brass stub. The remains of the anode may be waiting however to block the heat exchanger tubes. Betas can sometimes be a little on the limit when it comes to running temperatures so I would remove the end caps, heat exchanger and give it all a good clean out. I have found it pays to remove the heat exchanger every year, the end caps can be a ****** to remove if left too long. Doing it every year turns it into a simple easy job rather than a struggle. Replace antifreeze (my Beta20 only needs 3lts) new O rings (bit of silicon grease on them) every other year, new anode every season and it is neither expensive or arduous. I very much doubt you will have suffered any serious heat exchanger damage.
Would post a photo but my phone wont communicate with computer at the moment. The head of the anode holder has sheared leaving the brass threaded section stuck in the end cap housing - I take it there is a section of the anode material that goes right into the threaded part of the nut. I was able to insert a cotton bud right through the remains of the nut which is how i know the anode has gone. Thank you (and others) for pointing out there may be bits of anode stuck in the heat exchanger somewhere - I wouldn't have thought of that. So the question now is whether the brass thread has welded itself to the aluminium (?) end cap in which case new end cap required or if can be extracted without damaging the cap.
Now that's a pain. However, you should be able to get the thread out by drilling or cutting it across with a hacksaw blade at various points until you can knock the sections out. Depending on access, obviously best done with the H/E end cap, or whatever the thread is stuck in, on the bench.
