An 83-year-old woman died days after a burglary during which her life savings were stolen.
Four bogus water company staff tricked their way into Betsy Malpass's Dudley home in a "terrifying burglary" on 8 February, West Midlands Police said.
She was taken to hospital the following weekend and her final days were "dominated by stress".
The Crimestoppers charity is offering up to £5,000 for information leading to the conviction of those responsible.
It is believed the offenders arrived at her home in Corporation Road, Kates Hill, in a black Audi.
The suspects are all described as white men, police said.
The force said one was thought to be in his mid-20s and about 5ft 10ins tall with a chubby face. He was wearing a black hat and scarf.
Mrs Malpass died three days after being taken to hospital.
Daughter Lorraine Morris said: "It's heartbreaking really, when you go up and she (isn't) at home and then you just feel angry that they've (taken) her away from us."
Mrs Malpass's son Derek Malpass said: "There's still a lot of decent people out there and some of these people do know... who these people (are), from spending their money, enjoying themselves, bragging about it, because these sort of people do."
Crimestoppers spokesperson Gary Murray said the burglary "ended with terrible consequences after a wonderful older lady died".
He said: "She had suffered a horrendous ordeal in her own home, where she had lived independently.
"Her last days were dominated by the stress of this robbery and the loss of all of her life savings."
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