Former tenants of the Windemere Court Apartments had picketed a planned demolition of the complex, which was destroyed by fire back in January.
On Tuesday morning, Councilwoman Jannie Blackwell, who sought a court order to stop demolition on behalf of residents, told Action News that residents can now request specific items from recovery experts.
If the request is feasible, the experts will go into the building to search for the items.
City officials have said the building is unsafe and residents themselves are not allowed to go in.
The building owners released a statement on Tuesday morning saying they would work with the former residents, but that demolition remains the only option for the building.
Work to bring it down is expected to begin by the middle of the week.
A cause for this fire has yet to be determined.