The building is run by Mission Australia, with most residents having experienced long-term homelessness.
Residents asked those living with 5km of the building to "show solidarity", bring a rainbow or Aboriginal flag, and exercise underneath the Common Grounds housing estate on Saturday wearing purple or white.
NSW Police told SBS News it is aware "there is some activity" at the building this afternoon but "thus far there have been no arrests or charges."
Common Ground resident Ms Saffaa said the hard lockdown "should have been led by a public health response, not by police."
"We are being overpoliced in Common Ground and it has to stop," she said.
Robin, another resident in the building, drew comparisons to the hard lockdown in Melbourne's Flemington housing estate last July.
"We know that Flemington public housing estate in Victoria also has COVID cases and they are in semi-lockdown," Robin said.
Earlier this week, another Flemington public housing tower was added to the list of COVID-19 exposure sites. It comes after two nearby public housing towers were added to the list of exposure sites last month.
"Last year that estate was put in hard lockdown and horribly over-policed," he said.
"The Ombudsman requested the Victorian government apologise to the public housing residents they locked down without adequate food or medicines."
On Tuesday, The Feed spoke with Ms Saffaa, who claimed authorities had been searching care packages and deliveries to the building and confiscating items like alcohol and cigarettes.
The Feed put these claims to NSW Police and was advised to contact NSW Health who are managing the site.
A spokesperson at Sydney Local Health District confirmed that "some deliveries of alcohol have been restricted to ensure the safety of health staff and residents".
The spokesperson said the same alcohol consumption guidelines apply to people quarantining in the Special Health Accommodation "which cares for those who have been diagnosed with COVID-19 or close contacts or a confirmed case".
"Any alcohol deliveries that have been withheld will be available to residents when the building ceases to be in lockdown."
On Friday, a group of legal and human rights groups issued a statement condemning "the inappropriate policing and unlawful searches imposed on residents of Common Ground in Camperdown".
The open letter was signed by Amnesty International, NSW Council for Civil Liberties, Legal Observers NSW, Tenants Union NSW, Shelter NSW and Melbourne Activist Legal Support.
In it, the groups expressed concern about "the unlawful searches of residents' deliveries, seizure and confiscation of personal items and subsequent distribution of personal items to the wrong recipients".
The groups noted: "The Public Health (COVID-19 Self-Isolation) Order No 3 and the Public Health Act 2010 do not provide any express or implied powers for NSW Health or NSW Police to search or confiscate the belongings of individuals who are required to self-isolate, or to impose limits on their consumption of legal substances".
"This is a serious overreach of power that is particularly concerning in light of the misuse and continual extension of police powers during the COVID-19 pandemic."
In a press release on its website, Mission Australia said it welcomed "people's right to protest safely in accordance with Public Health Orders and the law."
“Mission Australia’s focus continues to be on providing ongoing support to our Common Ground tenants to ensure their safety and wellbeing during the lockdown and so they have access to everything they need at this time," a spokesperson said.
“We have staff onsite and offsite working around the clock to provide support to tenants and continue to work with NSW Health to ensure the safety of all tenants onsite.
“Additionally, tenants may be entitled to Centrelink income support if they have lost income or are experiencing financial hardship as a result of COVID-19 or this current lockdown. Our tenant care team is working with tenants to support them to access this income support.”