The report, Denial and Delay: The Impact of the Immigration Law's "Terrorism Bars" on Asylum Seekers and Refugees in the United States, shines light on the extent of the problem. At their core, the problems stem from an over-broad definition of 'material support' that snares a huge number of otherwise uncontroversial immigrants and asylum seekers in the category of terrorists.
Example: your father was kidnapped my a militant group in Zimbabwe and in order to save his life you had to pay his ransom. Upon his safe return you decide to seek asylum in the United States. Unfortunately, in the eyes of U.S. law the ransom is material support to a terrorist organization, and you are a terrorist.
From the HRF press release:
"These were not the people Congress intended to target," said Human Rights First's Anwen Hughes, author of the report. "In fact many of these refugees supported the same causes the United States supports, or were victimized by forces the U.S. government also opposes. But attempts to solve this problem through piecemeal "waiver" announcements are not working."
According to the report, over 18,000 refugees and asylum seekers have been affected by these overbroad provisions to date, and of those, over 7,500 cases remain on indefinite hold with the Department of Homeland Security. For the past four years, the Departments of Homeland Security, Justice, and State have been attempting to resolve this problem by granting discretionary "waivers" of the law's effects. Unfortunately, this approach has left many refugees in limbo and others at risk of deportation.
The press release and links to other materials including the report are here.