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Eliza was the mother of John, the landlord.
In 1947, she was terminally ill and the doctors had given up on her. However, her son brought her what he thought were insects from the garden to try to cheer her up. They were in fact space termites. Once she was left alone that night, the sound from her music box awakened them and they began transmuting her body into wood in order to preserve her before she died. (Knock Knock)
When her son discovered the space termites’ abilities, he tamed them and for the next seventy years would lure young people looking for accommodation to their house. The termites would then proceed to absorb the victims and transfer their life energies into Eliza to prolong her life. As he got older, John also told her that he was her father in order to prevent her from objecting to such an obscene decision, as the elongated life in isolation stunted her memory.
In 2017, Bill Potts and a few other classmates looking for student accommodation were invited by John into their house. Once the Twelfth Doctor, who was helping Bill move in, deduced something was amiss, the house proceeded to absorb Pavel, Paul and all the other students except for Bill and the Doctor, the latter of whom John had spared in the hope he could find a better solution to save Eliza.
Bill found Eliza first and witnessed a horrific display of the preservation process when the termites absorbed her friend. Eliza expressed regret over it but claimed she had no choice. John then arrived with the Doctor who offered his help. (Knock Knock)
After he pieced together what was happening, Eliza remembered the Landlord was in fact her now aged son John and was utterly horrified by all the people he had killed just so she could live. John, angered the pair had revealed his identity, proceeded to summon the termites to kill the Doctor and Bill. Eliza managed to use her connection to them to make them disperse. She then hugged her son and caused the termites to devour them in order to put an end to the madness.
As her last act, she also had the space termites restore Bill’s friends as she had never fed on their life energies, thus saving them. The termites then caused the entire house to disintegrate. (Knock Knock)
Eliza was a kind and compassionate young woman. Though the preservation made her slightly naive and believe that The Landlord was her father rather than her son, she eventually remembered and was horrified and disgusted by the lengths he had gone to just to keep her alive.
She had also grown immensely lonely during the seventy years of her preserved state. This was a deciding factor in her decision to kill herself and her son as she reasoned that life was not worth living if she was isolated and locked away from the rest of the world. (Knock Knock)