The Biden administration is fighting in court to preserve a Trump-era public health rule that uses the coronavirus pandemic to justify quickly turning back migrant families at the border with Mexico. According to the government, the rule is still needed to keep the virus from spreading in American communities and holding facilities, where migrants seeking asylum are typically held for days.

But immigration and human rights advocates say the rule, known as Title 42, is being used improperly as an enforcement tool, forcing migrants to return to dangerous situations. They have pressed President Biden to lift the rule, which was put in place by the Centers for Disease Control and Prevention. Some of the groups, including the American Civil Liberties Union, have sued the government to stop it from using the rule to expel migrant families.

In September, an appeals court panel stayed a lower court’s ruling blocking the policy for migrant families; oral arguments in the case are scheduled for mid-January.

From March 2020, when Title 42 was put in place, through the end of October, the measure has been used to turn back migrants 1.3 million times. But that number represents only 64 percent of the Border Patrol’s total encounters with people crossing illegally over the same time frame.

The result has been a confusing and chaotic approach to border security. Whether a person is permitted to stay in the United States at least temporarily or is turned back immediately under the public health rule can vary by hour or by day, as well as from one border crossing to the next.

The reinstatement this week of a different Trump-era policy that forces certain migrants to wait in Mexico while U.S. officials consider their claims is likely to add to the confusion. The United States has said it would place migrants into the Remain in Mexico program only if they could not be expelled using the ​Title 42 rule.

Here are the reasons that many migrants have been allowed to stay in the United States, despite Title 42.

Unaccompanied migrant children are allowed into the U.S.

During his first news conference as president, at the beginning of a sharp surge in illegal border crossings, Mr. Biden said, “The only people we’re not going to let sitting there, on the other side of the Rio Grande — by themselves, with no help — are children.”

In February, the C.D.C. exempted migrant children who arrive at the border without a parent or guardian from being expelled under Title 42. That has led to thousands of children staying weeks — and in some cases, months — in emergency shelters that were set up quickly to house them.

Under President Donald J. Trump, nearly 16,000 children who arrived alone were expelled under the public health rule. Nearly 137,500 were allowed into the United States between February and September this year, according to border data. The number of children arriving rose sharply when Mr. Biden took office, and they were exempted from the rule. The administration scrambled to build temporary shelters to house them.

As of Dec, 1, nearly 13,000 migrant children were in government custody.

Mexico does not have to accept all migrants who are expelled from the U.S.

In January, Mexico started enforcing a new law under which it cannot hold children under 12 in government custody. This forced the United States to temporarily admit some families with young children who had crossed illegally in South Texas.

Because U.S. immigration officials are limited in how long they can detain migrant children, they have released tens of thousands of families with instructions to report to immigration authorities.

Over the past year, nearly 480,000 migrants have crossed the border illegally as part of family units. But only about a quarter of them have been turned back under the public health rule. Most of the rest have been allowed into the United States temporarily, often under monitoring.

As of Oct. 28, more than 136,000 families were being tracked by Immigration and Customs Enforcement through ankle monitoring devices, online tracking and phone check-ins, according to government data analyzed by the Transactional Records Access Clearinghouse at Syracuse University.

Single adults have also been allowed into the country, despite the rule, though a lot less often. Of the more than 1.1 million times that single adults were caught crossing the border in the past year, Title 42 was used to expel them 84 percent of the time.

Border officials are overwhelmed.

The unusually high number of illegal border crossings has overwhelmed the government at times, with holding areas filled to capacity while officials conduct interviews and fill out paperwork. This has led to hundreds of thousands of migrants being released into the United States with instructions to report for enforcement proceedings.

Space is limited because of pandemic-related health precautions, but the number of migrants crossing illegally in the past 12 months, particularly since Mr. Biden took office, has set a 61-year record.

Republicans say the numbers have increased so sharply because Mr. Biden signaled during his presidential campaign that his administration would be more welcoming to migrants. Others say the public health rule is to blame; hundreds of thousands of people have tried to cross illegally multiple times, they say, because unlike in normal times, the expulsions do not come with significant legal consequences.

Expelling migrants under the public health rule is much faster — averaging about 15 minutes per person — than under normal circumstances, when questions and paperwork can take up to two hours, according to the Department of Homeland Security.

Particularly vulnerable migrants are granted humanitarian exemptions.

By early August, more than 16,000 migrants apprehended at the border had been granted humanitarian exemptions to the public health rule, allowing them to stay, the department said at the time. Advocacy groups and international organizations have deemed these migrants as vulnerable; they include transgender people and families with young children who live in dangerous places along the border.

But from the beginning, the program was a source of confusion.

“There’s no clear set of criteria for which families are allowed in,” Jessica Bolter, an analyst at the Migration Policy Institute, told NPR in May. “So it can really seem to migrants kind of like a game of chance.”

The humanitarian organizations that agreed to work with the Biden administration to help migrants seek such exemptions largely ended their participation over the summer, because they objected to the government’s continued use of the public health rule.

“We agreed to participate on a fixed-term basis to remove barriers and help as many people as possible access their right to seek international protection, with the expectation that the current administration would end the policy soon after,” Meghan Lopez, the International Rescue Committee’s regional vice president for Latin America, said in a statement on Oct. 18. “Months later, this still hasn’t happened,”

The Department of Homeland Security has not exercised this exemption since the organizations ended their participation, according to an administration official who spoke on the condition of anonymity to discuss the matter.

Some countries will not take back their citizens.

There have always been countries that refuse to take back their citizens. In 2006, China refused to take back about 39,000 citizens who would have otherwise been denied entry into the United States. The Department of Homeland Security released many of them to await immigration enforcement proceedings.

The United States faces the same challenge with other countries, such as Brazil, Cuba, Nicaragua and Venezuela. The number of people from those countries crossing illegally has increased. In October, Venezuelans were turned away under the public health rule 91 times, even though border officials caught Venezuelans crossing illegally more than 13,400 times. Similarly, Cubans were expelled only 42 times out of the nearly 6,000 who were caught crossing the border without documentation.

Now that the Biden administration is reinstating the Remain in Mexico program, some migrants from these countries could have to wait out their cases in Mexico instead of the United States. But because of humanitarian stipulations that Mexico demanded in order to cooperate, it is not likely to siphon off a significant number of migrants waiting out enforcement proceedings in the United States.

In October, half the migrants who were not expelled under Title 42 were from Brazil, Cuba, Nicaragua and Venezuela — countries that typically will not repatriate their citizens. Nearly half were traveling as part of a family unit or were unaccompanied children. Some families with young children and unaccompanied children are considered too vulnerable to wait in Mexico until their asylum cases are decided, and would therefore not be probable candidates for the Remain in Mexico program.