Other than the pedantic answer (any time Declarer can't possibly make), there are plenty of times that it doesn't have the impact you're suggesting.
First off, there are a lot of ways you can end up in a doubled contract. You might make a negative double and then your partner passes to convert to penalty, for example. That gives declarer some information, though, so I assume that's not in the spirit of your question. However, there are other possibilities...
- Auctions where opponents make a pre-emptive or sacrificial bid, where it is obvious that they will not make the contract to both defenders. In that case, a double is simply pro forma, and either player might make the double simply based on bidding position.
- Auctions where a double is optional (showing strength), and the responder passes the double, give only limited information to declarer since both players have shown something
- In some duplicate forms, there are auctions where it is clear both sides have a game, and one side must double the other side in the hope to set by enough to exceed the points likely made at the other table(s); again, that won't convey very much information.
Secondly, you certainly point out an example where one player knows of a problematic distribution for declarer, but it doesn't convey information as to which player has the trump stack. That's a risky bid, though, and I'd usually not make a double solely based on a trump lack or a trump stack, as it's not worth letting Declarer know there's a trump imbalance. A doubled contract where the double comes out of nowhere is a big "be careful" sign to declarer, and will inevitably make them more likely to make the contract than they would be if not doubled - even if they don't know who has the stack. And having 0 means partner could have 5 - or could have 2, and they could've underbid their 6-5 trump fit.
I don't think doubling based on opponents bidding a tight game, when you don't have anything special for yourself, is a great idea either; it can be appropriate in duplicate when you are in a competitive situation and they bid something that doesn't make sense - either you get enough points to compensate for you not getting the contract or they get a top board anyway - but it's still quite risky, and in the situation you describe (they having, say, (12-14) and (8-10) and you having 7, partner having 9-11) it seems like a poor choice as if they're in an unreasonable game you do well anyway, but obviously it's situational. Again, you're more likely to put them on high alert than anything else.
I think overall, though, any bid shows some information to both sides; it's the nature of bridge. The question is always whether you have conveyed information that is detrimental to your side in excess of the value of the information conveyed (or the points earned, in the case of the double). I don't think it's a good idea to double to "mislead", as first off you mislead everyone at the table partner included; and second, then you're just gambling, which is a bad idea unless you're really down and need a miracle.
