Three other people were injured when the HGV crashed into a house, smashing down one of the walls.
The vehicle was being followed by police at the time.
Four men were arrested after the lorry knocked down and killed Mrs Wileman, who was in her 50s.
It then hit two parked cars and smashed into the side of the house in Brierley, near Barnsley, South Yorkshire.
The incident, which happened in Park View at around 1.40pm on Friday, has been referred to the Independent Office for Police Conduct (IOPC).
In a statement, Mrs Wileman’s family said: “We are grateful to everyone for their kind messages of condolence and support so far.
“We would like to ask that you continue to respect our privacy as we come to terms with what has happened and grieve for Jacqueline.
“We would also like to express our thanks to those on Common Road and Park View yesterday who assisted at the scene.
“We ask anyone who was there, or who has any information, to please get in touch with the police so that they can bring those responsible to justice.”
A spokesman for South Yorkshire Police said the lorry had previously been reported as stolen.
He added: “It was travelling along Common Lane, towards Grimethorpe, when an officer in a marked patrol car travelling in the opposite direction, turned around to follow the vehicle.”
The spokesman confirmed that after the lorry hit Mrs Wileman, “the vehicle then hit two parked cars before colliding with a house on the road and coming to a stop”.
The newly-built house was severely damaged by the crash, with beds, clothing, televisions and other household items clearly visible from outside the property.
Witnesses said no-one was in the house at the time of the crash. However, the residents returned shortly after the incident to find their home wrecked. It is thought building work on the property only finished about six months ago.
People living nearby were alerted to the incident by “a loud bang”.
Witnesses said police arrived at the scene quickly and reported seeing men jumping out of the lorry cab and running away.
One man, who did not want to be named, said: “It’s come and hit two cars and then just crashed right into the house.
“It hit the woman near the cars. It’s just terrible.
“The police were following it and it was obviously going too fast.”
Another man said: “I was standing outside that house earlier. I just can’t believe it.”
An IOPC spokesman said: “We were notified by South Yorkshire Police about this incident at around 3pm.
“We sent our investigators to the scene and to the police post-incident procedure to gather information and assess the level, if any, of our future involvement.”
Anyone with information about the incident is asked to call 101.
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