At an unknown time and at an unknown location, Danelo Souza Cavalcante, a 34-year-old citizen of Brazil, entered the United States unlawfully — without being inspected or admitted by a U.S. immigration official, according to the Department of Homeland Security.

Sometime after that, in April 2021, prosecutors said he fatally stabbed his Brazilian girlfriend in front of her children in Pennsylvania, and he was convicted of murder and sentenced to life in prison. It was the second time he was accused of a horrific crime: He was fleeing a 2017 murder charge in Brazil when he entered the United States, the authorities said.

His escape from the Chester County Prison in Pennsylvania on Aug. 31 touched off a colossal manhunt, now entering its second week, and a host of questions about why Mr. Cavalcante had not been deported after his arrest in the United States — and whether, once captured, he would remain in a U.S. prison at taxpayers’ expense.

The case highlights an issue the criminal justice system has long confronted: the question of what happens when crimes are committed by undocumented immigrants, who studies show are much less likely to commit crimes than U.S.-born citizens.

Immigrants who are in the country illegally and are charged with relatively minor offenses are often sent back to their homelands. But for a variety of reasons, those facing serious crimes are most often required to serve their sentences in the United States.

In Mr. Cavalcante’s case, lawyers said, any decision on deporting him would most likely have to be postponed until after he had served out his sentence.

Did U.S. law enforcement know that a fugitive from Brazil was in the United States?

Most likely not. The United States is home to more than 11 million undocumented immigrants, most of whom intentionally stay in the shadows and steer clear of trouble with law enforcement or any contact with U.S. Immigration and Customs Enforcement, the agency that identifies and deports people who are in the country unlawfully.

“The primary way that ICE comes into contact with undocumented immigrants is if they have committed crimes,” said Aaron Reichlin-Melnick, policy director of the American Immigration Council in Washington.

Mr. Cavalcante was wanted in Brazil in connection with the slaying of a man in his small town of Figueiropolis in 2017.

Even if Brazil had issued an Interpol notice calling for his arrest, the United States would have had no reason to believe he was living in the United States.

Only after his arrest in connection with the murder of his girlfriend in April 2021 did ICE become aware that he was in the country, the agency said in a statement.

Which immigrants do federal authorities target for deportation?

Given limited enforcement resources and the large population of undocumented immigrants, the Biden administration has instructed federal officers to focus on immigrants considered a threat to national security or public safety, or who have recently crossed the border illegally.

In a policy memo to immigration agents two years ago, the Homeland Security secretary, Alejandro Mayorkas, directed agents to also take into consideration other factors in deciding whether to apprehend immigrants — such as whether they had lived in the United States for many years, were of advanced age or had U.S.-born children.

Mr. Mayorkas instructed immigration officers to employ “discretionary authority” in deciding who should be removed from the country.

A person who committed murder would clearly be a priority for enforcement, officials said.

What typically happens to immigrants who are arrested?

When noncitizens are arrested in connection with criminal activity by state or local authorities, ICE typically lodges what is known as an immigration detainer — a request that ICE be notified as early as possible before the person is released so that the agency can begin the process of deporting them.

An ICE detainer was indeed lodged against Mr. Cavalcante once he was arrested, according to an ICE spokesman.

In the 2022 fiscal year, ICE issued 78,829 detainers for noncitizens with criminal histories, including 1,751 for homicide-related offenses; 1,911 for kidnappings; 2,934 for robberies; 8,450 for sex crimes; and 26,186 for assaults. (The same person might have been charged with more than one crime.)

What kinds of crimes typically result in deportation?

A set of laws passed by Congress in the mid-1990s rendered noncitizens, including lawful permanent residents, deportable for many more types of crimes.

“U.S. immigration law is harsh to those with criminal convictions,” Mr. Reichlin-Melnick said. “The majority of felonies are deportable offenses under U.S. law.”

Undocumented immigrants who have committed minor infractions, such as driving with a broken taillight, and who are booked into a county jail, have been turned over to ICE and deported.

Immigrants caught driving under the influence of alcohol have been removed from the country. Many immigrants, including green-card holders who have resided in the United States for most of their lives, have been deported for dealing drugs.

In the 2022 fiscal year, ICE removed from the United States 28,204 people who had a criminal record. A large number of them were deported for immigration-related offenses, such as for re-entering the country illegally, second only to offenses related to illicit substances.

So is the Brazilian fugitive likely to be deported? If so, when?

People who are tried and convicted of a crime in the United States must serve their time here, with rare exceptions.

Because other countries are not required to jail people on the basis of U.S. convictions, keeping people imprisoned in the United States ensures that they serve their full sentence.

“If people were deported immediately after they were sentenced, it could end up being a get-out-of-jail free card, and that doesn’t make sense for our justice system,” said Mr. Reichlin-Melnick, a lawyer who previously represented immigrants in removal proceedings on the basis of criminal convictions.

“Foreign countries have no obligation to imprison people for U.S. crimes,” he said.

Are there exceptions for a case like the one in Pennsylvania?

An exception would be highly unlikely.

“Of course, with a life sentence, the question would be, what if we wanted to deport him instead?” said William Stock, a Philadelphia immigration lawyer.

There is a provision in immigration law that allows a state to request that a person be deported instead of incarcerated, but it applies only to nonviolent offenses.

“As a practical matter, that is rarely used because you wouldn’t want a person to be deported and not serve their sentence, which is a risk, if the person were sent to their home country where they have not been convicted of a crime,” said Mr. Stock, who is a past president of the American Immigration Lawyers Association.

It is unclear whether Brazil might request Mr. Cavalcante’s extradition on the pending murder charge there.

More likely, Mr. Stock said, Mr. Cavalcante, once captured, will remain incarcerated in Pennsylvania until he completes his sentence, though if he were ever paroled, he would almost surely be immediately handed over to immigration authorities to be deported.