SHENZHEN , China — China was on the cusp of the biggest building boom the world had ever seen when Zhang Zhiyang started his architecture firm. It was 2007, and the money rushed in for contracts to design residential complexes and an exhibition hall.

These days, with China’s economy slowing and his own business dropping off, Mr. Zhang can’t seem to get paid on time. He is now accepting the financial equivalent of i.o.u.s from as many as one-third of his clients instead of cash.

“It wasn’t like this before,” he said. But, he added, “it’s better than nothing.”

China’s trade war with the United States has escalated in recent days, posing a growing threat to an already slowing economy. Beijing needs private businesses like Mr. Zhang’s and his clients to help rekindle growth and provide paychecks to Chinese workers.

But many of those private businesses are short of cash. Instead, more than $200 billion in i.o.u.s — known in the dry world of finance as commercial acceptance bills — are floating around the Chinese financial system, according to government data.