Surrey County Council said Surrey Safeguarding Adults Board was investigating "this tragic event".
Ms Foster died on Monday. Her MP, Conservative Crispin Blunt, has described her ordeal as "horrific".
"I am very sorry to hear that Mrs Foster has now, sadly, passed away," he said. "Clearly there are questions to answer and I would expect a comprehensive investigation between all of the agencies involved.
"I said last week that I would certainly not like to pre-judge any more of the narrative before it is formally established. Yesterday's desperately sad developments can only increase the salience of that need."
Carefirst24 provided care to elderly people across Surrey and the London Borough of Sutton on behalf of the two local authorities.
UKBA raided its headquarters in Upper Mulgrave Road, Sutton, on 15 January as part of an investigation into suspected illegal workers and fraud Six people were arrested on suspicion of conspiracy to defraud and conspiracy to assist foreign nationals.
A spokeswoman for the county council said on Tuesday: "We are very sad to hear about Mrs Foster's death and our thoughts are with her family and friends at this difficult time The safety of vulnerable adults is our top priority, which is why this tragic event is already being urgently looked at by the Surrey Safeguarding Adults Board."
The spokeswoman said she did not know how long the investigation by the safeguarding board, set up to protect vulnerable adults, would take.
As well as the county council, its members include Surrey Police, NHS Surrey, the 11 district and borough councils in Surrey and voluntary sector organisations such as Mencap, the Surrey Coalition of Service Users and Action for Carers.
A spokeswoman for AGE UK Surrey said lessons must be learnt from Ms Foster's case.
Paul Burstow, Lib Dem MP for Sutton and Cheam, said Surrey County Council needed to get to the bottom of why its procedures did not work properly.
Telephones at Carefirst24's offices are not being answered and no reply has been received to inquiries by email.
All those arrested have been bailed until dates in April.