The two are wanted in Santa Barbara on felony vandalism charges. They are pursuing refugee status, and their case is pending in a Canadian court.
In an exclusive interview with Good Morning America's Andrea Canning, the couple said they fear they'll be killed if they leave Canada for California.
The Quaids said people would want to kill them so that it would be easier to take their money.
"They follow us, they tail us, they tag our cell phone, they hack our computer," said the actor
The Quaids call them "star whackers," an exclusive circle in Hollywood that they blame for their problems and other celebrity scandals, even deaths.
"It is very possible that Heath Ledger could have been murdered, or David Carradine," said the actor.
Ledger was found unresponsive in his New York home in 2008, and Carradine was found dead in Thailand in 2009.
When asked who the "star whackers" are, Evi Quaid responded, "They are business men. They're absolute businessmen. It's the mafia, It's organized crime."
Regarding tapes in which Gibson is heard going on tirades, Evi Quaid said, "I think he was drugged. I think he was slipped a mickey."
When they were asked about their mental health, the Quaids denied speculations that either of them are mentally unstable, schizophrenic or on drugs.
The actor said he and his wife are not faking anything.
"We're just trying to find some safety, some security" said Randy Quaid.