A sample of asylum cases, granted and denied, reflects some of the inconsistencies.

Joël Kangudi, 34, Congo

Mr. Kangudi, an information technology technician and gospel singer, fled the Democratic Republic of Congo after he released a song on YouTube criticizing human rights abuses by the government. Authorities in Congo arrested Mr. Kangudi, locked him up and tortured him. He walked across a bridge to El Paso in 2017, then spent four months in a detention center in New Mexico before gaining asylum.

M. P., 30s, El Salvador

M. P. and her son, J. G., fled El Salvador in 2014 after the MS-13 gang tried several times to recruit him and vowed to kill the teenager’s mother unless he joined. They entered the United States illegally and applied for asylum in 2016 in Utah. A judge denied her request in March on the grounds that claims of gang violence do not qualify for asylum, but M. P. is appealing. She is unable to work and is afraid she could be deported at any moment, said her lawyer, Christina Brown of Denver. Her son is part of the same application. (They did not want be identified because they feared it could jeopardize their case.)

Cristina Bebawy, 62, Morocco

Moroccan police officers raided the apartment where Ms. Bebawy, a teacher, participated in Bible studies in 2009. She and other women there were arrested and thrown into jail, where they were forced to undress and perform sex acts. The officers videotaped and photographed the acts, then used the footage to justify arresting the women multiple times. Ms. Bebawy received asylum after traveling to the United States on a tourist visa in 2013, according to her lawyer, Christopher Casazza, in Wayne, Pa.

Che Eric Sama, 28, Cameroon

Mr. Sama, a university student from Cameroon, applied for asylum after fleeing first to Nigeria, then traveling through Mexico to the United States border in 2015. He said he had been beaten by an anti-gay group for posting a statement in a student publication in support of gay rights in Cameroon, where same-sex sexual activity is illegal and punishable by prison. Mr. Sama, who claimed he faced the possibility of state-sanctioned harm if he was forced to return to Cameroon, had his request for asylum denied, in addition to his appeal in April. He has been deported.

Yomara Rivas, 27, Guatemala

Ms. Rivas fled to the United States with her daughter, then 4, in 2014, making a perilous trek from Guatemala to the Arizona desert. Ms. Rivas, who was born into an impoverished family of coffee pickers, said in her asylum request that her boyfriend had become physically abusive and tried to strangle their daughter. Ms. Rivas was granted asylum before Jeff Sessions, the attorney general, signaled that he opposes giving asylum to domestic violence victims.

M. C., Honduras

M. C. was detained in South Texas in 2015 and requested asylum as a victim of domestic violence. She passed her credible-fear interview but then remained in detention for nine months. A judge rejected her application, contending that the Honduran government was instituting policies to address domestic violence. She filed an appeal, which was denied on similar grounds, and is appealing again. The board of immigration appeals sent the case back to the same judge, who has since retired. Her case may be heard again in 2020. M. C. cannot work and is living with her child in New Jersey, relying on family to support them. (She asked not to be identified to avoid jeopardizing her case.)