I do get that in the end that Malorie and her kids end up in an old school for the blind which happens to house lots of birds, but it's a school in the end.
But why is this movie named 'Bird Box'? Is there any significance to this name?
A bird box, also known as a nest box, is a man-made enclosure to allow animals a place to nest.
A nest box, also spelled nestbox, is a man-made enclosure provided for animals to nest in. Nest boxes are most frequently utilized for birds, in which case they are also called birdhouses or a birdbox/bird box, but some mammalian species may also use them. Placing nestboxes or roosting boxes may also be used to help maintain populations of particular species in an area. The nest box was invented by the British conservationist Charles Waterton in the early 19th century to encourage more birdlife and wildfowl on the nature reserve he set up on his estate.
Although I have yet to see the film (or read the book), I do know that it is a horror survivalist story about not being able to look at an entity and this then plays on themes about examining motherhood/maternal instincts and the nature of man vs the nature of animals with there being a literal bird box for human beings...
They (all people shown at the end) are enclosed in that building just like birds in a bird box. So the building is the bird box for them.