Can TODA ever be shorter than TORA, under any circumstance?
No

Takeoff Distance Available (TODA) can never be shorter than Takeoff Run Available (TORA).

AIM 4-3-6 


  Takeoff Distance Available (TODA) – The takeoff run available plus the length of any remaining runway or clearway beyond the far end of the takeoff run available.


I had previously downloaded the FAA runway database and determined there is no TODA less than TORA.  The mysterious airport may have incorrect data or the database is incorrect.

FAA Airport Information

The same database shows that approximately 14% of the runways have an ASDA shorter than TORA.  Multi-engine pilots need to be aware of how their aircrafts performance was created and how to apply the correct declared distances.