This phenomenon, of course, is not unknown in the courts, as you may well appreciate. The recourse to take is to go to the court for an order—it used to be, anyway; I've not been in the courts for a while and maybe there's a simpler process now. We used to have to go back in front of a judge and get an order for what was called substituted service. Then you get an order saying “post a notice in the local newspaper for this many days over this many weeks” or “leave it at this certain address and that address”. And if you do those things, then the courts will deem the person to have been served.
Now we don't have that kind of process here, but it could well be the case that if the committee were to report to the House that these steps were taken to try to effect service, the House, in its judgment, could simply deem the person to have been served, and in my view, that would be sufficient for purposes of the House proceedings.