Which is correct?

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

2 answers

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

:-)