BRASÍLIA—President-elect Jair Bolsonaro vows to make significant cuts to Brazil’s bloated, indebted state—and the fate of an array of government-owned companies hangs in the balance.

Brazil’s government is involved in a range of businesses. It owns or has a stake in Latin America’s largest produce and fish wholesaler, a condom factory in the Amazon, banks, real estate agencies, drugmakers, hospitals and a firm created years ago to build a $16 billion bullet train that never became a reality.