Interesting post...
When the Trust is not renewed, the aircraft reverts back to the non American owner. When there is a non American owner, the FAA de-registeres the aircraft
As an aside, how does the FAA find out? Presumably only if the Trustee tells them.
This came up on the other thread, regarding Graham Hill, whose N-reg Aztec had at some point become de-registered. I thought it was possibly caused by somebody in the Hill camp applying to the FAA for an Export CofA (but not preceeding with it) but now that you mention it it could have simply been a non-payment of the trust fee followed by a lack of communication.