But she says that didn't prevent a policeman from hitting her in the face on 7 July as she was taking part in a peaceful antigovernment protest on the anniversary of her husband's disappearance.
"People were literally scared. They were shouting: 'She is the wife, the wife. Don't touch her; she is the wife. They are [Zavadski's] relatives.' There was complete silence; everybody was shocked. I think everyone took it to mean that if they hit me, anybody else could just be trampled or shot," Zavadskaya said.
The Belarusian Interior Ministry denies Zavadskaya's account of the incident. They say it was she who attacked the policeman during the demonstration on a central street in the capital Minsk.
But Zavadskaya says she still remembers the face of the police officer who struck her. "I remember that he was of average stature, not very tall. He was very unpleasant," she said. "I don't know how to say it, but he had nothing human in his eyes. He had something brutal in his eyes. He looked as if I had done something wrong to him personally."
The small crowd of some 40 demonstrators was quickly dispersed. But questions persist concerning police conduct. Analysts and other observers say police brutality is commonplace in Belarus.
Tatyana Protko, the head of the Belarusian Helsinki Committee, an independent human rights organization, told RFE/RL that antigovernment demonstrations usually end in violence, with protests forcefully dispersed. "Any demonstration, if it opposes the authorities or is not organized by them, ends up in the beating or detention of those who participate," she said.
Protko's organization files regular reports to the UN Human Rights Committee on incidents involving police brutality. She says the special police forces who deal with public demonstrations are particularly violent -- as well as loyal to authoritarian President Alyaksandr Lukashenka.
"The president demonstrates his affection to them. On TV, they show the president mixing with them. He comes personally to check various unit, he shoots weapons together with them. He praises them and so on. They have good salaries," Protko said.
But ordinary police officers are guilty of abusive behavior as well. Alyaksandr Sosnou, the deputy director of the Minsk-based Independent Institute of Socioeconomic and Political Studies (NISEPI), says they often suffer from what he calls a Soviet-style mind-set.
"Usually they don't have enough education and understand very little about life. They may even rob people -- that also happens, especially if the person is drunk and appears to be an intellectual," Sosnou said.
Sosnou says his institute has conducted a number of polls showing that the police are the least popular institution in the country. "We usually ask our respondents if they trust different state and public institutions," he said. "We also ask about the police. As a rule, the police finds themselves at the bottom of the list."
But little change is expected for now. Sosnou says that until Belarus's entire political system is based on democratic principles, there is no reason to expect a reform of law enforcement and police conduct.