In October 1997 Joe Cinque was killed by his girlfriend, Anu Singh, in their Downer flat.
Ms Singh, then 25, injected her boyfriend, 26-year-old Joe Cinque with a lethal dose of heroin.
Today, the flat at 79 Antill Street is vacant and has been for some time. Last week, fencing was put up in preparation for demolition.
ACT Housing purchased the unit for $710,000 in May 2016. A development application to knock down the flat and make way for public housing was lodged later that year.
The residence was among four properties, 79-85 Antill Street, marked for demolition.
The proposal was approved in February this year and a builder contracted in April.
Singh was acquitted of murder in 1999 on the basis of diminished responsibility. Instead, she was charged with manslaughter and served four years of a 10-year sentence.
Click here to read more.