Democrats there may follow the lead of those in North Carolina with lawsuits that could cast uncertainty over the exercise of power for several years.

The legal issue has to do with the separation of powers, said Allison Riggs, senior attorney at the Southern Coalition for Social Justice, a nonprofit dedicated to protecting rights for minorities.

“The legislature gets to make the laws, but when the legislature starts to try and undermine the ability of the governor to effectuate and implement the laws, they’re getting out of their lane,” Ms. Riggs said. If, for example, “control of the Board of Elections is taken away from him and instead is more vested in the legislature,” she added, “then the legislature becomes the one who’s trying to implement the laws, and that’s an executive duty.”

North Carolina’s courts have almost universally agreed with that argument. But the legal battles are still dragging on, largely because the legislature has responded to many of the judicial rebukes by passing slightly different versions of the same measure, which are then litigated all over again. In the meantime, the state operates under many of the challenged rules, and a cloud of uncertainty.

The effects of that uncertainty have been on display in the past week, as reports of election fraud rocked the state’s Ninth Congressional District. The elections board, which is investigating, has the authority to order a new election if it believes irregularities “taint the results of the entire election and cast doubt on its fairness.” But the board itself is in turmoil because a state judge recently ruled that its composition, as established by Republican changes in 2016, unconstitutionally limited Mr. Cooper’s power. By court order, the board is set to be dissolved next week, though a judge could extend that deadline.