The conclusion of the story suggests that this race doesn’t actually exist but what if it did?
Such a species would differ from the Silence, who are artificially created and don’t so much remain out of view but make you forget you have seen them. This is a species that is never seen.
The closest anyone comes is when they either start talking to themselves or awaken in the night, convinced that there is something under the bed (and there is). This could be due to the latent sixth sense that humans possess, that makes them aware of the other life form even when it goes undetected by their other senses.
Since this is a species that needs a skill to hide we can assume that it doesn’t involve invisibility or camouflage. If the entity in Rupert Pink’s room was one of these creatures it is visible (to the camera) and has a physical body.
Therefore this is a race who are just very good at finding places to conceal themselves. It is possible that they can move quickly and can either anticipate when someone might be looking in their direction or use a limited form of telepathy to detect where people are looking.
This race could be silent or just very good at making every sound they make match some of the ambient noise in the vicinity. This could be mimicking behaviour, copying the sounds of rattling pipes and creaking floorboards to cover their movement.
There could be some places they avoid, like wide open spaces, knowing that there wouldn’t be anywhere to hide. Orson Pink is afraid of what is outside the ship, rather than what is already there. This would indicate that they don’t normally enter confined spaces. The TARDIS is the exception due to its much bigger interior.
The implication is that these creatures follow everyone. Does this mean that they have a parasitic or symbiotic relationship with the person they are stalking? Do they feed of them or do they both benefit from the hidden races presence? What if their subject is killed or manages to leave them behind?
The entity in Rupert’s room appears to be child sized. If it was bonded to Rupert it could mean that each time a child is born so is a member of the unknown race. The pair age together.
This could explain why the species only reveal themselves to the very young or the very old. If they match the age of the subject they will be inexperienced when the observer is young and their physical condition will be in decline when the observer is old.
It could be that there are far fewer of this species. Rather than staying with Rupert his whole life, for example, the entity might linger at the children’s home. This could allow it a never ending number of children to pair with.
One of the acts the Doctor connects with this race is moving cups of coffee. We might suppose that the hidden race pick a subject to gather food and drink for them, taking what they need when no one is looking.
Yet the Doctor also believes that at the end of time this mysterious race will still be alive. The would indicate that they can endure when most other organic species would be wiped out.
The hidden race might gain skills from observing their subject. If one of these creatures is responsible for leaving the chalk board message in the TARDIS it might have learnt how to write from the Doctor himself, thus explaining why Clara believes it is his hand writing.
The Doctor also attributes a television turning off on its own to the unseen species. Did it do this physically or can they remotely control machinery, in much the same way that the Weeping Angels can turn off electrical lights?
It is notable that the references to people having dreams of monsters under the bed only occurs in human history. It could be that they only occur on Earth, evolving in line with humanity. The Doctor could picked up his ‘companion’ during a visit to Earth.
By their very nature we don’t get a clear view of this race. The one behind Clara in the children’s home is short and apparently hairless. The Doctor is initially terrified to have anyone look at it as it must never be seen.
It could be that its appearance is so unnatural, so abhorrent, that looking at it would drive someone insane. It could upset the natural order of reality so that the observer dies, is eradicated or erased from reality. It might send the being into a murderous frenzy.
The race don’t appear to be hostile. Indeed, they are not directly or indirectly responsible for any harm to others. The mere fact they exist is what frightens people. Left alone they peacefully live alongside humanity.
The fear that people experience around them could be artificial generated. This could be a a defence mechanism, persuading those affected to either flee or not dare look in the races direction.
When asked what such a race would do the answer left on the chalk board is ‘listen’. Does this indicate that the species spend most of the time listening to humanity. Do they do this for comfort or to gather information to use against them? Might they listen for other sources of danger in order to protect humanity?
Similarly to the above the entity in Rupert Pink’s bedroom can be communicated with. It takes no further action against three who clearly know it is there because they promise they won’t look.
If such a race really does exist humanity might be able to open a dialogue with it. Humanity might acknowledge they know the other race exist but be willing to co-exist (since they’ve lived in peace for so long).
For a planet that is routinely invaded by aliens having a native species that can go undetected could be beneficial. As long as this hidden species is willing to take action they can be persuaded to pass vital information to the humans and sabotage invasion efforts (since both benefit from repelling the invasion).
In this interpretation of events in this story this does mean that there is still one (if no more) of this race within the TARDIS. When the Doctor travels alone they will be waiting in the shadows and now they know the lengths he will go to in order to find them.