Hurricane Florence has killed at least 17 people and set rainfall records across the state. It was not clear how long he had been stranded.
One route into the city was reopened by midday on Monday, officials said.
Photos from the site provided to AP by Cape Fear River Watch, an environmental advocacy group, show cascades of gray-colored water spilling from at least two breaches at the landfill and flowing toward Sutton Lake, the plant's former cooling pond which is now used for public recreation, including fishing and boating.
Almost 20 rivers in the Carolinas were expected to crest in major flood stage this week, the Weather Channel said.
In some places, the rain stopped after Florence moved on, and the sun peeked through, but North Carolina governor Roy Cooper urged residents evacuated from the hardest-hit areas to stay away because of closed roads and flooding.
In Wilmington, the state's eighth-largest city, residents waited for hours outside stores and restaurants for basic necessities like water.
County commission chairman Woody White said officials were planning for food and water to be flown into the coastal city, located on a peninsula with the rising Cape Fear River to the west and more water to the east.
"As you can tell, they're not listening to me", he said.
Mayor Bill Saffo said he was working with the governor's office to get more fuel into Wilmington.
Ten tropical storms have formed this season in the Atlantic, five of which have been hurricanes, the National Hurricane Center said.
Since Matthew, Goldsboro has trained firefighters in water rescues and equipped them with additional boats, Stevens said, saying the city was "much better prepared with equipment and training to help people".
The problem was water, and lots of it, in Wilmington. The smell of broken pine trees wafted through damaged neighbourhoods.
More than 80,000 people in North Carolina already were without power as the storm began buffeting the coast, and more than 12,000 were in shelters.
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"It's all kind of a blur", Monroe said.
Florence, a onetime hurricane that weakened to a tropical depression by Sunday, is expected to decline in force again on Monday before re-intensifying on Tuesday and Wednesday, the U.S. National Hurricane Center said.
The forecast for Florence has not changed, unfortunately: It's still raining, and rivers are still rising.
With Florence moving west at 8 miles per hour, with maximum sustained winds of 35 miles per hour, the National Weather Service is warning of sustained risk from life-threatening floods, landslides, downed trees and power lines.
Something else to worry about: some dams might not be able to hold up under the strain of the devastating flooding in North Carolina.
The death toll climbed to at least 21 as authorities found the body of a one-year-old boy who was swept away after his mother drove into floodwaters and lost her grip on him while trying to get back to dry land, and an 88-year-old man's vehicle was swept off a road by floodwaters.
In all, a wide swath of North Carolina and a small part of SC saw three-day rainfall totals that, on average, would be expected to occur about every 1,000 years, the Weather Underground reported.
Florence, once a fearsome Category 4 hurricane, was still massive.
Forecasters said that given the storm's size and sluggish track, it could cause epic damage akin to what the Houston area saw during just over a year ago, with floodwaters swamping homes and businesses and washing over industrial waste sites and hog-manure ponds.
"While there are more than 3,000 active lagoons in the state that have been unaffected by the storm, we remain concerned about the potential impact of these record-shattering floods", the pork council's statement said.
Emergency officials had difficulty keeping up with the scope of the spreading disaster.
Julie Lamb, with her 15-month-old twins, stepped off a Coast Guard boat after being rescued from her parents' house, where the yard was submerged and water was still rising at Lumberton.