A runner makes run on a server protected by two ices. The second one is Nebula. The runner uses the Eater to break all subroutines on the first ice. Than runner encounters Nebula and it destroys eater. What happens with the Eaters effect "you cannot access more than 0 cards for the remainder of this run". Nothing?
You still wouldn't be able to access cards, because conditional effects of cards do not disappear when the card is trashed. Same way as with Sneakdoor Beta - if you start a run with it then it gets trashes midrun, you still apply it's access replacement effect for this run.