David Turner, who had worked for British Steel at Bescott, was a Conservative councillor for the Brownhills area on Walsall Metropolitan Council for 15 years.
His sister Anne Hawks said that her 67-year-old brother had had his Covid vaccination just days before he fell ill.
He had been living in the Rectory Gardens sheltered accommodation in Aldridge after recovering from illness.
But, with underlying health conditions, Mr Turner - who had been shielding all year - had booked himself into a care home for a month or so for recuperation.
“He had been very well looked after by carers at the sheltered accommodation and was well looked after in the home - which had never had a case of of coronavirus,” Mrs Hawks said.
“We were able to chat to him through the window via our phones during visits to the care home. He was happy and looked better than he had done in ages."
In the middle of last month Mr Turner received his first Covid vaccination along with others at the home.
“A few days afterwards, on the Wednesday he developed a cough and on the Thursday was diagnosed as having bronchitis with Covid.”
He was taken to the Manor Hospital and died within eight days, on January 29.
Mrs Hawks added: “David’s death shows that you just can’t be too careful. People really should not underestimate this virus. David had been so careful.
"He had regained his health after being ill although it had left him with underlying health conditions.”