What was Sara's back story?

Sarah's father killed her mother in front of her.

It was a ridiculous leap to believe that Matt would accept this stranger, a female, into his house when he knows he would be considered the first suspect in his wife's death. And what kind of weirdo foists herself upon a family in trauma? Too many instances of suspending disbelief are required to get through this muck of a show. As an aside - good acting, bad writing.