Mica McNeill and team mate Mica Moore had resorted to crowd-funding to raise more than 30,000 pounds ($40,296) after being told there was no budget to get them to South Korea.
The British Bobsleigh and Skeleton Association (BBSA) said in a statement that Parker would not be replaced and some cash would now be available.
"Richard had recently proposed a new structure for the next Olympic cycle but has left earlier than originally planned to help reduce central costs and ensure that maximum available resources can be focused on our athletes and their journey to February’s Olympic Winter Games," it said.
"Those resources mean that we can now partially support a GB Women’s bobsled to compete on the World Cup circuit and press for qualification."
The BBSA said it would work with McNeill and other athletes to identify areas where they required support throughout the season.
"That support will include coaching, medical and logistical assistance and will help underpin athletes' own admirable fund-raising efforts," it said.
Women's bobsleigh was added to the Olympic programme at the 2002 Salt Lake City Games and Britain has yet to win a medal in it. The men have won four medals over the years, including two-man gold in 1964 and a four-man bronze in 1998.
McNeill, a silver medallist at the 2012 Youth Winter Olympics, had said when launching her crowd funding initiative that the BBSA was funding three men's crews but had told her the women were not medal potential.
"I said, 'Why don't you just be honest and say you're not funding us because there's no money?', and they said, 'Yes, it's because there's no money -- if there was we'd be funding you'," she added.
(Reporting by Alan Baldwin, editing by Toby Davis)
