The U.S. immigration laws do not set a limit on the number of people who can be awarded asylum in the United States each year. The number of asylum grants varies, depending on how many people apply (either of their own volition or as a defense to deportation), and how many of them are successful with their asylum claim.
Don't be confused by the fact that there is a limit on the number of people who can be awarded refugee status each year. The U.S. president establishes this limit on an annual basis. Although the grounds for receiving asylum status and refugee status are the same (as set forth in the refugee definition found in § 101(a)(42) of the Immigration and Nationality Act or I.N.A., or 8 U.S.C. § 1101(a)(42)), the procedural requirements are different, and these two categories are treated differently.
See below for further discussion of the distinction between asylum status and refugee status.
The number of asylees tends to run about 25,000 per year. To get the latest figures on how many people have been awarded asylum as well as refugee status in given years, go to the Department of Homeland Security's website, which includes a page on Immigration Statistics. Look for the latest "Refugees and Asylees" report.
The United States provides refuge to people from other countries who are unable or unwilling to return to those countries because they have either been persecuted in the past or have a "well-founded" fear of future persecution. The persecution may be either by their government or by forces beyond the government's control. The basis for the persecution must be either the applicant's race, religion, nationality, political opinion, or membership in a particular social group (or a combination thereof).
Asylum allows people to apply for this protection upon or after their arrival in the United States (though under the Trump Administration, people attempting to apply at the Mexican border have been either placed into detention facilities or forced to wait in Mexico while applying).
The law says that people can apply whether they arrive legally (with a visa and inspection at a border or other point of entry) or illegally (without inspection). They can either submit an affirmative application within a year of entry or apply as a defense to either expedited removal (upon entry) or other placement in removal proceedings (for example, after apprehension by U.S. immigration authorities within the U.S.).
People granted asylum receive the to right to live in the U.S. for as long as they qualify as asylees. They also may apply for a work permit. After a year of approval, asylees can apply for a U.S. green card.
People who are outside the U.S. and seek protection based on past or future persecution must apply for refugee status, usually with the help of the U.N. High Commissioner for Refugees, and through overseas offices of U.S. Citizenship and Immigration Services.
In the past, the annual limits on refugees set by the U.S. president tended to range from between 70,000 and 90,000 admissions. However, the Trump Administration has drastically reduced this, setting an annual limit for 2019 of 30,000 refugee admissions.