What connection is there between the Palmer's estate of Cleveland in Sense and Sensibility and real Palmers who had died out leaving the Duchy of Cleveland without an heir?

There is no direct connection between the fictional Palmer's estate of Cleveland in Jane Austen's Sense and Sensibility and the real Palmers who had died out, thus leaving the Duchy of Cleveland without an heir. The similarity in names is likely a coincidence, and there is no established link between the two.