She doesn't have direct descendents, but you are correct in calling them living relatives.
They would be related through the grandparents of Andrew, Richard and Patty, who had 10 children, 9 surviving: Andrew's aunts and uncles.
They would also be related through Sarah Morse's family, as she had at least 11 siblings, not all living to marriage.
Because one has to go to Andrew's grandparents to find a relation, passing up siblings, but only to Sarah's brothers and sisters, I think the Morse bond is closer. And yes, Joe here and I have been in phone and e-mail contact with a living relative, who did know about the connection and was somewhat interested.
If one approaches the relation with the fact that Lizzie was acquitted, it makes it easier to communicate.
Actually I was the one asked: did I think she did it?
Since I've never really made up my mind, I can honestly answer she was acquitted. Since they were not really acquainted with all the facts, we did talk a lot about their own, more modern, family history- which was more interesting to me.
We probably know more about the case than any living relative.