> Any alien who is physically present in the United States or who arrives in the United States (whether or not at a designated port of arrival and including an alien who is brought to the United States after having been interdicted in international or United States waters), irrespective of such alien's status, may apply for asylum in accordance with this section or, where applicable, section 1225(b) of this title.
US law explicitly allows crossing the border not at a point of entry and without visa for the purpose of applying for political asylum.
That says you can apply for asylum regardless of entering illegally (or to use the term of art, EWI/entered without inspection). You can also apply if you are in removal proceedings for some other reason, ex. illegal work or false statements.
In and of itself, nothing in that statue allows or removes criminal or monetary penalties for the act of crossing illegally itself. There are cases where people were convicted of the same despite a successful grant of defensive asylum. (https://repository.uchastings.edu/cgi/viewcontent.cgi?articl...)
