Sure, use nothing. Let the "active load" discharge the capacitor as it will. Presumably the load will continue draining it below 2V, so I don't really know how anything should go "unused"...
If you have more specific scales of time and current in mind here, in terms of what counts as "absorb", "minimum energy", "completely", "discharge", "minimum voltage" and so on, a more useful answer may be possible.
Tim