A new voluntary buyback program for Mr Fluffy properties will be set up by the ACT government, as the current scheme is due to finish in August.
But the about 10 homeowners who have refused to sign up to the existing scheme will not be eligible for the new program, and could be forced from their homes after 2025.
Under the scheme that started in 2014, properties found to contain Mr Fluffy asbestos are bought and demolished by the ACT government.
The new scheme is effectively a continuation of the old scheme, but the new program will only apply to properties that are found to have Mr Fluffy asbestos after August 18, 2021.
Homeowners eligible for the current scheme who do not sign up by August 17 will not be able to take part in the new one.
ACT Sustainable Building Minister Rebecca Vassarotti said those homeowners would still have access to transition assistance but would face the potential of compulsory acquisition from 2025.
"We are very aware that for some people this is their long loved house and so we really do want to work with people to make it easy as possible for them," she said.
"From 2025, there will be the potential of compulsory acquisition, we do need to work to an end point of ensuring we are not placing the community at risk in relation to that.
"In managing that process, we will work very closely with households to ensure that they are looked after."
Ms Vassarotti said it was likely that more Mr Fluffy homes would be found in Canberra's older suburbs.
"Offering a voluntary buyback program similar to the existing program, that has been in place since 2014, commits to providing a far and equitable response to homeowners of properties after 17 August 2021," Ms Vassarotti said.
Under the existing scheme, there have been 1027 properties found to have Mr Fluffy asbestos. Of those, 992 had been demolished, either within the ACT government's scheme or privately, as of April 2021.
Of the 35 properties that remain, 11 have been surrendered to the government and demolition planning was underway and about 14 were set to be surrendered to the government.
People who remain in Mr Fluffy properties are required to have an asbestos management plan and there are building approval restrictions.
Ms Vassarotti introduced the proposed legislation amendments to make way for the new program to the ACT's parliament on Thursday morning.
The territory's Mr Fluffy blocks were first publicly identified in 2015. At the time there were 1022 blocks but this has since grown by five.
