The Houthi alliance with Mr. Saleh’s political party, the General People’s Congress, also gave the rebels a wider political base than they otherwise would have had.
But in the end, Mr. Saleh denounced the Houthis and said he wanted to turn a “new page” with Saudi Arabia to end the war. On Dec. 4, the Houthis killed him for it.
Saudi Arabia and the Houthis’ other enemies had long sought to split Mr. Saleh and the rebels, believing that the Houthis’ forces would fold easily if Mr. Saleh’s loyalists turned against them. But they were unprepared to capitalize on the situation when it actually happened, and the Houthis have since done all they can to make sure that Mr. Saleh’s remaining loyalists pose no threat.
That has led to the crackdown in Sana, and other Houthi-controlled areas, with Houthi fighters arresting hundreds of Mr. Saleh’s loyalists and locking them up, said Adel al-Shoga, a leader of Mr. Saleh’s party who is in Cairo.
About 45 of the party’s top 50 leaders are still in Sana, he said, and about 15 of them are under house arrest. The rest are in hiding, looking for ways to sneak themselves and their families out of the city.
“They are living in fear,” Mr. Shoga said of his wife and children, who remain in the city. “They spend every minute wondering if they will get caught.”
Mr. Saleh’s killing came after he had established new contacts with Saudi Arabia and its allies, which hoped that he and his loyalists could turn the tide of the war. Even Western nations like the United States had hoped that Mr. Saleh’s party could play a role in negotiations to end the conflict, which began in 2014 when the Houthis and forces loyal to Mr. Saleh seized Sana, later sending the internationally recognized government into exile.
A few months later, a coalition led by Saudi Arabia began a punishing bombing campaign that has failed to push the Houthis back while intensifying a humanitarian crisis.
But members of Mr. Saleh’s party interviewed recently said that instead of turning the party against the Houthis, Mr. Saleh’s death had shattered it.
The General People’s Congress was never really united by a shared vision as much as it was held together by Mr. Saleh’s leadership and his ability to distribute patronage, analysts said. Once he was gone, little held the group together.
Even though many members seethed at the Houthis for killing Mr. Saleh, few wanted to change sides and join the Saudi-led coalition that had been bombing them for years. And those who may have wanted to fight the Houthis lacked the ability to do so.
“There is deep depression occupying most of the people after the departure of Saleh, whom they saw as the last solution to get rid of the crisis,” said Asem Alshamiri, a Yemeni journalist in Sana who is close to the party.
“The capital is witnessing the worst days in terms of the humanitarian, psychological, military and political situation, and anxiety is hovering over everyone,” he said.
Many Houthis, too, believe they have destroyed Mr. Saleh’s party.
“The party is dead,” said Ahmed Abdel-Wali Dahab, a Houthi commander reached by phone. “The ones who are under house arrest are obviously not going to reach out to anyone, and they can’t go anywhere. And everyone else is on the run.”
To keep their enemies from conspiring against them, the Houthis have used their control of Yemen’s communications infrastructure to shut off access to the internet for days on end and to block social media sites like Facebook.
“It is not hard,” Mr. Dahab said. “We have telecommunication companies in Sana full of people who have been educated abroad. We had to stop our enemies from communicating with each other.”
Some analysts predict that the political isolation of the Houthis will catch up with them, either because the opposition to their rule will become too hard to manage or because they will run out of money, leaving them unable to provide services in areas where they are the de facto government.
The areas under their control already suffer dire electricity shortages, which have contributed to the world’s worst contemporary outbreak of cholera. And many civil servants have not received salaries in more than a year, pushing many families that used to be middle class into poverty.
The Saudi-led coalition has sought other ways to increase the pressure on the Houthis.
This month, Crown Prince Mohammed bin Salman of Saudi Arabia and Mohammed bin Zayed al-Nahyan, the crown prince of Abu Dhabi in the United Arab Emirates, met with leaders from Islah, the political party long considered the Yemeni branch of the Muslim Brotherhood, which Saudi Arabia and the U.A.E. consider a terrorist organization.
U.A.E. officials said the party had broken ties with the international Muslim Brotherhood, which was apparently enough of a guarantee for the Persian Gulf nations in their search for allies.
Abdelwahab al-Anasi, the secretary general of Islah, said by phone from Riyadh, the Saudi capital, that the meeting was a “turning point,” and that the party had been asked to reach out to remnants of Mr. Saleh’s party to see about working with them against the Houthis.
So far, they have had little luck.
“We are simply having an extremely difficult time reaching them,” Mr. Anasi said. “These are confusing times. It will take a while for us to get a clear picture of what is actually happening in Sana.”