They're being screened for deportation this week and according to their lawyers the government is fast-tracking their removal.
Hong Kong was once a safe place for asylum seeker Ajith Pushpakumara.
He fled to the territory after being tortured for deserting the Sri Lankan army. Now he says authorities from his home country are looking for him here, forcing him to change addresses.
"I was scared living in the old place. I quickly moved to a new place and never show anybody where it is," Mr Pushpakumara said.
The 43-year-old was one of four asylum seekers who sheltered Edward Snowden for two weeks when he was hiding in Hong Kong in 2013.
Snowden, a former intelligence contractor, fled the US after leaking surveillance secrets. The asylum seekers' identities were revealed after the release of a film about Snowden last year.
Lawyer Robert Tibbo says the Hong Kong government is failing to protect Mr Pushpakumara and the other families who assisted Snowden.
They include Sri Lankan national Supun Thilina Kellapatha, his wife Nadeeka Dilrukshi Nonis and their two children, and Filipino Vanessa Rodel and her daughter.
Mr Tibbo, who also represents Snowden, believes the Hong Kong government is targeting his clients for their role in Snowden's escape.
"The Hong Kong government questioned Ms Rodel about Mr Snowden. She refused and upon her refusal they started cutting off humanitarian assistance to her," Mr Tibbo said.
"We didn't expect the Hong Kong government to take such an adverse approach to my clients, for actually having done nothing wrong. Simply providing refuge to a man who was in need."
On March 9 Mr Tibbo and his legal team announced that they were appealing to Canada to accept the families as asylum seekers.
Within hours they each received letters from Hong Kong's immigration authorities informing them of their Removal Assessment Screenings, scheduled for this week.
"We're very concerned that the Hong Kong government is just rushing this with a view to remove them from Hong," Mr Tibbo said, adding that his clients could be deported in a matter of weeks.
From a press conference in Montreal on Wednesday lawyer Marc-Andre Seguin and his colleagues urged the Canadian government to expedite their consideration of the Snowden asylum seekers.
"Our clients have come to illustrate the ill treatment that Hong Kong imposes to asylum seekers to their territory," Mr Seguin said.
"For Hong Kong they are an embarrassment to be discarded, no matter the fate that awaits them in their country of origin.
"Now more than ever we need to demonstrate to the world that Canadians, and Montrealers, welcome refugees."
Hong Kong has one of the lowest asylum seeker acceptance rates in the world - less than one per cent since 1992.
Many asylum seekers in the territory often wait years for processing and rely on welfare as they're not permitted to work.
