Born in 1946 and brought up in Cupar, Fife, I was educated at the local school - 
Those affected are currently forced to choose between claiming damages for themselves or allowing relatives to claim after their death.
The Mesothelioma Damages Bill is to be amended to enable people to benefit from its provisions from 20 December.
The unusual move is thought to be unprecedented.
Deputy Justice Minister Johann Lamont made the announcement to MSPs on Holyrood's Justice 1 Committee, who are scrutinising the proposed legislation.
"Mesothelioma is a devastating disease - a cancer for which there is no cure," she said. "It can develop many years after exposure to asbestos and when it does, can kill fast.
"It is only right that we do all we can to minimise the distress this problem causes to those suffering from this disease and to their families as speedily as possible."
The move came about following consultation with families' representatives.
The bill will allow a victim's immediate family to claim damages, even if the deceased settled a claim while alive.
The amendment will mean that from next Wednesday mesothelioma sufferers will be able to proceed with their own claim in the knowledge that their families will not be disadvantaged.
The change was welcomed by SNP MSP Stewart Stevenson.
"Sufferers from this dreadful, and invariably fatal, disease will now have their wait for justice much shortened," he said.
The amendment was also welcomed by solicitor Frank Maguire from Thompsons Solicitors, which represents the majority of asbestos victims in Scotland.
"This is tremendous news for all those suffering from mesothelioma who have elected to die without claiming damages for themselves so as not to disadvantage their families," he said.
He added that he would now begin proceedings for about 100 cases.
Harry McCluskey, of Clydeside Action on Asbestos, described the move as tremendous news for victims and their families.
"It will end the terrible dilemma they faced of having to claim for themselves and deprive their families, or choosing to die without claiming to protect their families' rights," he said.
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