Students Barnaby and Grace, and caretaker Ian Coates, were stabbed to death on 13 June 2023 by Calocane, who had been diagnosed with paranoid schizophrenia in 2020.
Calocane was convicted of manslaughter on the basis of diminished responsibility, and detained at a high-security hospital.
Barnaby's mother, Emma Webber, said: "This is long overdue, and simply the right thing to do.
"It was a disgrace that Calocane and offenders like him have ever received taxpayers' money.
"A hospital bed does not erase the egregious crimes committed, nor the destruction they have caused.
"Closing this loophole finally delivers some basic accountability that victims deserve."
Dr Sanjoy Kumar, Grace's father, said: "Our campaign has always been about accountability and fairness.
"Offenders with treatment orders already cost the taxpayer an enormous amount.
"On release, every offender gets help with housing and benefits.
"On the principle of fairness alone, we do not see why taxpayers should fund benefits while they are incarcerated."
The government said the move followed engagement with victims' families and experts as part of its plan to "put fairness back of the heart of the welfare system".
Work and Pensions Secretary Pat McFadden said: "We said we'd act to tackle this gross unfairness and we're delivering on that promise.
"For too long these violent criminals have had their living costs paid by the taxpayer twice over, while their victims and families paid the price.
"That ends today because victims and taxpayers deserve a system that is fair and supports only those who genuinely need it."
Shadow Work and Pensions Secretary Helen Whately said: "Killers and rapists should not pocket benefits from a hospital bed.
"Labour has taken all year to stop a loophole it promised to close. And tens of millions saved barely makes a dent in the benefits bill Labour has let spiral out of control.
"The Conservatives would make universal credit a conditional, time-limited benefit, so taxpayers' money goes only to those who genuinely need it."
The proposed regulations apply to individuals subject to a Section 37 order under the Mental Health Act 1983 and a Section 57A order under the Criminal Procedure (Scotland) Act 1995.
The offences covered include manslaughter, attempted murder, wounding with intent to cause grievous bodily harm, rape, assault by penetration and rape of a child under 13.
Murder is not included because a hospital order is not an available sentence for the offence.
The change in regulation is expected to affect about 2,500 offenders already in hospital and approximately 200 a year in future, the government said, with the full financial impacts of the move due to be published as part of the 2026 Budget on 28 October.