But Environment, Planning and Sustainable Development Directorate deputy director-general Geoffrey Rutledge believes the government is well-prepared to deal with any future finds.

In July, a tradesperson made the first Mr Fluffy discovery in the ACT for nearly three years when they found "suspicious material" in the roof cavity of a home in Curtin.

According to the ACT Asbestos Response Taskforce's affected residential premises register, the owners of that property have already surrendered their lease to the territory government. Their buyback offer was based on July 2019 prices, reflecting the date the property was added to the affected residential premises register.

"It's clear from that property that we saw in Curtin that there is probably still loose-fill asbestos in our community, and the government will need to respond to those [properties] case-by-case," Mr Rutledge said this week.

"What we saw with that most recent property is they contacted the taskforce, as we would expect anyone to, and we were able to help that family with their specific solution.

"[A Mr Fluffy discovery] could happen again. I won't guarantee that it won't. But when it does, the Asbestos Response Taskforce is well-equipped to deal with that."

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Mr Rutledge was speaking after the ACT government announced a number of measures that will come into play at the end of the Mr Fluffy buyback and demolition scheme on June 30 next year.

There are 37 privately owned Mr Fluffy homes known to still be standing in Canberra, with 20 of those expected to surrender their leases to the government on or before June 30, 2020.

While the ACT government maintains that all homes affected by the potentially deadly loose-fill asbestos must be demolished, it will not force people from their homes immediately at the end of the buyback and demolition scheme. Compulsory acquisition will only be considered on a case-by-case basis from mid-2025.

Mr Rutledge said he was confident all affected homes would be demolished by then after the government unveiled "pathways to eradication", including a transition assistance program, targeted at breaking down the barriers that have prevented the remaining homeowners from taking part in the buyback and demolition scheme.

But he may be in for a surprise, with Lyons homeowner Lorraine Carvalho joining Aranda resident Jean Geue in vowing to fight to remain beyond 2025.

Mrs Carvalho said she was willing to negotiate a deal with the government and just wanted an offer that reflected the true value of her property, having turned down the initial buyback offer because she believed it was unfair.

She said homeowners had never had any choice. The government's position had been to make an offer and effectively say, 'Take it or leave it'.

"We're not holding out for top dollar," Mrs Carvalho said. "We just want replacement value for [the property]."

She said the government should have planned the entire scheme from the outset, rather than waiting more than five years after it was first announced to say there would be no compulsory acquisitions until at least mid-2025.

Former Mr Fluffy homeowner Felicity Prideaux, who is also a spokeswoman for the Mr Fluffy Full Disclosure group, agreed.

She said many homeowners, including herself, would probably have made different decisions had they known they would not be immediately forced from their homes at the end of the scheme.

The original deadline to sign up to the buyback and demolition scheme was June 30, 2015 - just eight months after then-chief minister Katy Gallagher said all affected homes would need to be knocked down.

Mrs Prideaux said she and others signed up quickly because they did not want to risk being left with nothing if the government pursued compulsory acquisition.

"What [the uncertainty] did was instill fear into a lot of people," she said.

Mrs Prideaux urged the government to publicly detail how it would handle any compulsory acquisitions, and what deals it would offer the owners of any Mr Fluffy houses that are still to be discovered.