The woman, named in reports as Claire McCabe was rushed to hospital after falling ill on Saturday evening during a hot tub party at a farmhouse in Selkirk.
Police have said that the death is being treated as ‘unexplained’ with inquiries ongoing.
Claire was one of many who had attended the farmhouse as part of birthday celebrations for Graeme Steel.
Claire, who is believed to have one child, took ill at the party and was rushed to Edinburgh’s Royal Infirmary.
A police spokesman said: “We are investigating after a 44-year-old woman took unwell at an address in Stow during the evening of September 1, before passing away at the Royal Infirmary later that night.
“The death is currently being treated as unexplained but not suspicious and inquiries are continuing.”
Graeme is one of Lord Steel’s three children.
Lord Steel, 80, led the Liberal Party from 1976 to 1988, when he helped merge his party with the SDP to form what became the Liberal Democrats.
He was also the first presiding officer of the Scottish Parliament, serving between 1999 and 2003.