A police spokesman would not say which beneficiaries they would deem dangerous.
The "exact detail" would be worked through between police, the Ministry of Justice and the Ministry of Social Development.
A spokeswoman for Police Minister Anne Tolley said the police commissioner would have the discretion to decide where he saw a risk to thepublic.
Auckland Action Against Poverty spokeswoman Sarah Thompson said there were problems with the policy.
"Firstly, many people who have a warrant out for their arrest may not even be aware of this until their benefit is cut.
"These people are yet to be convicted of anything, and even if they were to be they would still receive their benefit unless they were imprisoned, which most people are not.
"So she will be effectively sanctioning many people who, even once tried, would have continued to receive their benefit.
"The fact that, as Bennett herself says, most people clear their warrants within 30 days points to the idea that she is releasing policies like this for no major outcome other than to distract the public from her department's continued failure to decrease poverty and unemployment."
Mrs Bennett said 58 per cent of people with outstanding warrants cleared them within 28 days.
The new rules would given them an extra 10 days to clear or challenge the warrant before their benefit was stopped.
Beneficiaries could still apply for hardship assistance for themselves and their children.
