SFA chief executive Stewart Regan says they take full responsibility for child protection failings.
Plan To Protect Prisoners' Children
Labour has unveiled a new Bill aimed at tackling the "devastating'' impact a prison sentence can have on the children of offenders.
The party wants to change the law to ensure that children who have a parent in prison get additional support at school.
Scottish leader Jim Murphy insisted the proposals were not about "being soft on crime or telling judges to be lenient on criminals with children''.
He argued: "If someone has committed a crime, then they should be punished - not their children.''
The Bill is launched after Justice Secretary Michael Matheson announced ministers were scrapping plans to build a new women-only jail in Inverclyde, and were instead looking at alternative options.
Mr Murphy highlighted concerns that when "a parent goes to jail, and particularly when it's a mother, the impact on the children can sometimes be devastating''.
He said: "We need to recognise that children with a parent in prison are more likely to go on to commit a crime themselves later on in life and suffer from mental health problems. They are victims of circumstance who need support, and should not be punished for things outwith their control.
"This Bill is the next step in Scottish Labour's plans to reform our justice system so that it punishes crime, not vulnerable families and children. I hope it gets the support it deserves from across civic Scotland.''
Labour MSP Mary Fee, who has introduced the Support for Children (Impact of Parental Imprisonment) (Scotland) Bill at Holyrood, said the children of prisoners were the "forgotten victims'' of the justice system who are "unseen and go without support''.
She stated: "My Bill will attempt to make sure these children are given the support they need.
"When a parent is sentenced, my Bill will ensure a needs assessment of their child is carried out right away. It will also guarantee that the difficulties faced by children with a parent in prison are recognised in school.''
Ms Fee insisted: "No child should be punished for the actions of their parent. We need a fairer system so every child has the best chance of getting on in life and this Bill is a step closer to delivering it.''
Martin Crewe, director of the charity Barnardo's Scotland, welcomed the proposals and said: "We know from our work with families that children affected by parental imprisonment are an extremely vulnerable group who often suffer in silence, are unseen and unheard.
"We welcome the announcement by Mary Fee MSP to publish a Member's Bill consultation which proposes ways in which children affected by parental imprisonment could be assessed and supported.
"The Scottish Government has put a renewed focus on looking at radical ways to deal with female offenders, 66% of whom have children. We very much hope that what appears to be a growing cross-party consensus on this issue is used to ensure that children affected by parental imprisonment no longer have to go unsupported and unrecognised.''
Matt Forde, head of service for NSPCC Scotland, said: "This Bill marks an important step forward in improving the life experiences of this vulnerable group. By recognising the specific needs of children with a parent in prison, and their care givers, the best possible support can be provided to ensure consistent care and a healthy, happy start in life.''
The 55-year-old died at the scene of the incident in Dryden Street at about 9.50am on Monday.
She called on both sides of the Brexit divide to treat each other with respect and stop accusations of "racism''.
Police found the body of Sharon Greenop at a house in Aldersyde Avenue, Troon, South Ayrshire, on November 10.
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