A Brisbane man accused of murdering his American girlfriend might not be a killer at all — because she could still be out there, living her life "below the radar."

Mark Sheridan Waden, 50, has spent two weeks on trial in Brisbane Supreme Court for the alleged murder of Priscilla Brooten, a 46-year-old US citizen who disappeared in 2018. But in his closing statement on Friday, defence barrister James Godbolt told the jury the case is built on sand.

"The investigation is inadequate in the extreme," Godbolt said.

He argued that police searches for Brooten had "a not high level of reliability." The prosecution's case relies on the assumption she is dead, but Godbolt says there's no solid evidence she isn't alive and well — just hard to find.

Brooten, he explained, was in Australia illegally for years and deliberately stayed off the grid. She had no bank account, no Centrelink account, no Medicare card, and no mobile phone in her own name. She used seven known aliases. Police relied on other organisations to run searches for those aliases, and came up empty.

"She is someone who doesn't want to be found," Godbolt said.

"The investigation is inadequate in the extreme."

The prosecution tells a very different story. Crown prosecutor Andrew Walklate said Waden killed Brooten when their troubled relationship "came to a head" over money and infidelity. He allegedly buried her in a trench at his home in Brisbane's northern suburbs on July 5, 2018, then dug her up almost a year later and dumped her body at a rubbish tip.

Walklate pointed to Waden's behaviour after Brooten vanished. He lied to her friends, saying she'd been raided by Border Force and deported. He impersonated her in messages. He dug a trench. He removed hundreds of kilograms of soil from his yard, drove it to a tip at night, and pressure-washed his trailer afterwards.

"That is not the conduct of a man dealing with the aftermath of a momentary unlawful assault," Walklate said. "It was the intention to cause at least serious bodily harm."

But Godbolt countered that Waden was working late shifts as an Uber driver at the time and could only run errands at night. He also noted that claims of decaying human remains at Waden's home weren't backed by witness testimony or forensic evidence.

The defence raised another possibility: suicide. Brooten had consulted a doctor and a psychologist about serious self-harm and major depression.

"Unfortunately it does loom in this case the possibility of suicide," Godbolt said.

Jurors will begin deliberating on Monday after receiving directions from Justice Peter Callaghan.

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