Consider a standard Stern-Gerlach setup. An electron with mixed up/down spin is sent through a magnetic field. Then there are electron detectors that detect whether it went up or down.
Now, the up detector is connected to a very loud bell. The down detector is connected to a dim light. On the standard consciousness-causes-collapse (ccc) theory, if there is an observer who can both hear and see, she collapses the wavefunction, with probabilities given by the Born rule.
But now suppose that our observer has fallen asleep. The bell would wake the observer. The light wouldn't. What happens?
I think that if we accept ccc, we should also accept that the wavefunction collapses in this case. Thus, sometimes the wavefunction collapses in favor of up and a bell, and sometimes it collapses in favor of down and a light. In the latter case, there is no observation made—the observer is unconscious. Thus, on this solution, while an unconscious observer is capable of collapsing a wavefunction.
Perhaps one disagrees that the wavefunction collapses here. Then the observer in the lab is in a superposition of awake and asleep states. This by itself seems unacceptable. It seems that the whole point of ccc was to ensure that we did not have to worry about the weirdness of superpositions between different conscious states. But a superposition between a conscious and a non-conscious state is just as weird. Moreover, supposing that our observer is in a superposition of awake and asleep states, we can imagine a second observer coming into the lab. As soon as the second observer notes whether the first is asleep, we will have collapse. If that happens, then suddenly the first observer comes to be in a pure state. Some of the time, that pure state will be one of remembering being woken up by a bell. But that memory is false: she was never woken up by a bell, but was in a superposition of woken and non-woken states. So this interpretation leads to us having to attribute false memories to observers. And we should avoid that.
This line of thought suggests that we should treat non-observation as a kind of observation. Collapse happens whether the bell is observed or not. Collapse occurs always to exclude superpositions between different observational states, where non-observation counts as an observational state.
Suppose we do this outside of quantum mechanics? Well, this could have some implications for Sleeping Beauty. It would suggest that the Sleeping Beauty problem where one is woken on Monday and Tuesday on tails (with amnesia induced in between) and only on Monday on heads is equivalent to the variant where on heads one is also woken on Tuesday and informed that there was heads. For the non-observation on heads on Tuesday in the first problem should be thought of as a kind of observation. I think thirding is quite plausible on the variant on standard Bayesian grounds, so this supports thirding in the original.
We also get a variant of that lighthearted answer to verificationist worries about Christianity. The lighthearted answer is that whether Christianity is true is verifiable. Just wait until you're dead, and you'll see. Well, not quite, goes the riposte: you will see if there is an afterlife, but if there is no afterlife, you won't. But if we treat non-observation as a kind of observation, then you in effect do "observe"—through genuine observation if there is an afterlife and without one otherwise.
How far do we take the principle that non-observation can count as observation? Do non-observations by non-existent persons count? Quite possibly. Suppose that a lab apparatus is set up so that a conscious being is produced when the up electron detector is triggered and not otherwise. Similar reasoning to the above suggests that we should have collapse here, even if no conscious being is produced. The mere possibility of producing one triggers collapse.
Of course, ccc may be false.