Lillian Oluk, 36, and her two-year-old daughter Lynne Mutumba were found dead in their one-bedroom flat.
A harrowing inquest was told there was no medical reason for their deaths but various examinations suggested Lillian was suffering from malnutrition and starvation and little Lynne had been dehydrated.
They had no food in the house and no possessions other than the clothes on their back, the court heard.
Lillian was also not taking her medication for HIV and sickle cell anaemia when they were found at their flat in Gillingham, Kent, on March 14.
Coroner Kate Thomas recorded open verdicts into their deaths following the inquest at Old Gravesend Town Hall. She said there was not enough evidence to say for certain how they had died.
The coroner had been told that Lillian and Lynne had moved to Gillingham on December 10.
Until the middle of February, Lillian was buying healthy food for the pair of them using a money pass from social services, but this seemed to have stopped by February 14.
After that, she did not buy groceries and for two weeks they appear to have existed on takeaways, visiting McDonalds or KFC twice a day.
The inquest was told there was no evidence of the mother having bought any food after February 28.
CCTV footage shows Lillian leaving the flat and going to the communal bins but there were no sightings of her after March 7.
Lillian was last seen with Lynne on February 28 coming back from a local church and she was last seen on her own on March 7 when she met her key worker. When the bodies were discovered, Lynne was in bed and her mum was on the floor of the bedroom.
Lillian originally came from Uganda and used to work for LSG Sky Chefs, a company that supplies catering and supplies for airlines, based near Gatwick Airport.
The inquest was told that in mid-February she received a letter telling her she was no longer entitled to stay in this country.
She came to the attention of social services in Croydon when she and Lynne were camping out at the local hospital for two weeks.
She was found a home in Wolverhampton but the flat was unsuitable and she was moved to Gillingham in December.
At the end of the inquest, Ms Thomas said it was a "tragic set of circumstances whatever they were".