Final answer:
The people who broke away from the HBC and NWC were known as Freemen or Otipemisiwak, a group seeking independence from the fur trade companies.
Step-by-step explanation:
The individuals who broke away from the constraints of the Hudson's Bay Company (HBC) and the North West Company (NWC) were known as Freemen or Otipemisiwak. These groups consisted of individuals of European and Indigenous descent, often referred to as Metis, who sought to live independently of the fur trade companies by which they were formerly employed. They engaged in trade on their own terms, demonstrating autonomy and resistance to the control that the HBC and NWC exerted over the fur trade and the people involved in it.