At one point there was a rules ruling via e-mail that it wouldn't be trashed to OverSight AI, and separately that Chum wouldn't do the damage. In the latest FAQ It has been clarified that this didn't make sense, and so for consistency "all" would apply to "0" and so all the subroutines are broken, and so chum does not do damage and oversight AI means the ice is trashed.
The word “all” includes the number zero.
The Corporation plays an OversightAI
and rezzes a Woodcutter. The Runner encounters the Woodcutter while it has
zero subroutines. The Runner is considered to have broken all the
subroutines on the Woodcutter, and the ice is trashed.
(Previously, it was decided that since there were no subroutines the number broken was unknowable and so effects wouldn't trigger, but that gets rather confusing rather quickly with rules effectively throwing null pointer exceptions!)