Halliday & Matthiessen (2004: 501, 502):
This too has provided the resources for another tense form and another modality. … Originally two verbal groups, it is now either
(i) + done, a secondary tense form ‘past in’ … or
(ii) + to do, a modal form (of the ‘modulation’ type) … .
In other words, ‘possessing’ a process, if combined with past/passive, means past (success); if combined with ‘unreal’, it means (future) obligation.