Guzda said the male acquaintance was a contractor who was doing work on the home. The Stamford Advocate reported that the contractor is Michael Borcina, who was taken to Stamford Hospital and remained in stable condition as of Monday afternoon.
Badger, an ad executive in the fashion industry, is the founder of Badger & Winters Group.
Neighbor Charles Mangano said he saw rescuers walking Badger and the man away from the house toward an ambulance.
"I heard her say 'My whole life is in there,' as she walked out," Mangano said. "They were both obviously in a state of shock."
Neighbors in the Shippan Point neighborhood said they were awakened by screaming and ran outside to see fire consuming the house.
Stamford Fire Chief Antonio Conte said firefighters were called at 4:52 a.m. and arrived to find the house engulfed in flames. The first-arriving firefighters were able to get Badger and Borcina out of the house, but despite several efforts could not reach the five people trapped inside.
"There was so much flame and heat it drove the firefighters back," Conte said. "They tried several times. We knew all five were in there. We just couldn't get to them."
Conte became emotional as he talked about the fire and its heavy toll.
"I've been on this job 38 years," he said. "Not an easy day."
The house was razed around 8 a.m. Monday. The Stamford fire marshal's office has not released the cause of the fire.
Badger bought the three-story, 3,300-square-foot, five-bedroom house that overlooks Long Island Sound" href="http://www.courant.com/topic/travel/long-island-sound-HPL9.topic">Long Island Sound in December 2010 for $1.72 million. The house had been undergoing extensive renovations, neighbors said.
The lot where the house once stood was covered with charred debris and cordoned off by police with tape on Monday. Passersby left bouquets, stuffed animals and candles nearby.
Gov. Dannel Malloy " href="http://www.courant.com/topic/politics/government/dannel-malloy--PEPLT00007625.topic">Dannel P. Malloy, a former mayor of Stamford, offered his condolences to Badger and her family in a statement and said her loss "defies explanation."
The fire was Stamford's deadliest since a 1987 blaze that also killed five people, Conte said.
Badger gained fame for Calvin Klein underwear and Obsession perfume ads featuring Kate Moss" href="http://www.courant.com/topic/human-interest/kate-moss-PECLB0040854545.topic">Kate Moss. She founded Badger & Winters Group at age 30.
Associated Press reports are included in this story.