Whether the first lady’s power will survive her husband’s death is unclear. She is reported to head one of the two competing factions inside ZANU-PF, but is she its leader, or just a useful puppet for veteran survivors of Zimbabwean politics? After her husband dies, will she hop on a plane for Dubai or elsewhere in Asia, where she and her children have established homes? The Mugabes are thought to have more than $1 billion invested outside Zimbabwe, according to an American diplomatic cable released by WikiLeaks.

But if she succeeds in grabbing power, it would most likely be a continuation of her husband’s government. Changes critical to reviving Zimbabwe’s crumpled economy, including land reform, are thought politically impossible under Mr. Mugabe and would remain so under Ms. Mugabe, whose legitimacy derives from her husband’s legacy. Her elevation could also intensify tensions in Zimbabwe’s small political class by upsetting Mr. Mugabe’s lieutenants, many of whom have been waiting decades to take over.

Confident of their grip on power, the Mugabes flew out of Zimbabwe a few days after the end of the congress in mid-December for their annual extended holiday in Asia, where Mr. Mugabe is thought to have received medical care in Singapore and Malaysia, and where the first family owns real estate in Hong Kong.

Ms. Mugabe left for her latest holiday even though she was embroiled in a dispute with a Lebanese diamond dealer over a $1.35 million ring. According to a court document, Ms. Mugabe ordered the diamond from the dealer; issued the payment from a bank in Harare, the Zimbabwean capital; then canceled her purchase after the diamond had already been prepared. Ms. Mugabe demanded that the dealer refund the money to a bank account in Dubai, according to the court document.

The dealer, Jamal Ahmed, said he had refused to transfer the money to Dubai because it would be considered money laundering, but agreed to reimburse the first lady in installments, according to an affidavit submitted to the High Court of Zimbabwe. Men associated with Ms. Mugabe and her son from a previous marriage subsequently seized and occupied three of the dealer’s properties in Harare.

Wilson Manase, Ms. Mugabe’s lawyer, did not return calls and messages to his cellphone.

Ms. Mugabe had picked the diamond as her husband’s 20th wedding anniversary present to her.