In order to seek asylum in the USA (and every other country), the process is exactly the same as that for immigraiton. You have to apply beforehand. You do not enter the border with a passport or walk across the border. They might have entered with a passport, but that is not the process used to seek asylum.

Also, to be an asylum seeker, one has to be a political figure, or have done something for which the government wants you.

These were 'undocumented workers.' I don't think you know a things about entering different countries. I used to be an immigrant to the USA. I left after 11 years. I have lived in multiple countries on three continents, and I know how the system works.

So, please give me a list of these 'asylum seekers.' I don't believe it for one moment. I also want to know why they have a price on their head.

https://www.uscis.gov/humanitarian/refugees-and-asylum/asylum#