Which is correct?

Question

.....and her family is unable to pay for it by themselves.
or
.....and her family is unable to pay for it by itself.

Answer 1

The second sentence is correct. We assume that in this case that the family is one unit.

Answer 2

but you will also often hear

and her family are unable to pay for it by themselves.

where the family is treated as a group of people. (family are treated?)

:-)