Mr. Smith, who since taking office two years ago has operated under the principle that not even a powerful ex-president is above the law, now finds himself on the defensive as he rushes to wind down a pair of complex investigations slowed by the courts and ultimately made moot by Mr. Trump’s electoral victory.

Mr. Smith’s office is still drawing up its plan for how to end the cases, and it is possible that unforeseen circumstances — such as judicial rulings or decisions by other government officials — could alter his intended timeline. But Mr. Smith is trying to finish his work and leave before Mr. Trump returns to power, the people familiar with his plans said.