Owner Jane Bryant is in the process of taking the building down per court order, after a four-year battle over code violations at the dilapidated two-story complex built in 1925.
Ms Bryant was never able to realise her dream to renovate the building after buying it in 2007. She has been salvaging building materials and selling off items from Oswald's three-room apartment. The toilet already has a new owner.
Oswald lived there from November 1962 to March 1963. The residence is mentioned in the Warren Commission report.
The report said Oswald acted alone on November 22, 1963, when firing at Mr Kennedy's motorcade from the Texas School Book Depository's sixth floor.