At another house in the neighborhood, they got as far as wiring the down payment. But the sellers changed their minds and refused to accept the money.

“Our life savings were sitting in purgatory for three days,” Ms. Clay said. “We had told everybody and celebrated. That was a heartbreak.”

Then one day, while aimlessly surfing real estate sites, Ms. Clay found a curious for-sale-by-owner listing. “Talking to the owner felt like talking to a family friend,” she said. “He grew up in the house with his three siblings. His family owned it their whole life.”

She went for a visit. “The house had good vibes, but it was super-outdated,” she said, with orange kitchen cabinets and dark wood paneling. And at $1.2 million, the price seemed high. Also, she was preoccupied with a trip to Europe they were planning a few days later.

At the airport, however, the couple discovered that Ms. Clay’s passport was invalid — it expired in five months, rather than the requisite six, which meant they had to obtain an expedited passport and fly out two days later.

“That ride back to our apartment was a real low point,” said Mr. Wolfram, who was planning a surprise proposal in Paris.

With an unexpected day free, Ms. Clay suggested they both go to see the house. “It had this worn, dusty coat, but it had this warmth about it,” Mr. Wolfram said.