Asylum is an immigration status for people who are in danger of persecution - the threat of severe harm or death - if they return to their country of origin.
Every way to enter the United States - with a visa, parole, asking to enter at the border, or crossing the border "without inspection - is the "right way" to claim asylum. There is no way of entering the US that makes someone ineligible for asylum.
Many people who are seeking asylum have been held in immigration detention. Having been in detention does not make someone a criminal, and does not mean they did something wrong or illegal.
The process of waiting for a decision on an asylum claim usually takes between 3 and 8 years.
While asylum seekers are waiting for a decision on their case, they are generally not eligible for federal benefits like social security, unemployment, housing assistance, and food stamps.
An asylum applicant must wait 150 days after their asylum application is filed before even applying for a work permit. Without a work permit, a person is not eligible to work for a US employer.
By the time they arrive, most people seeking asylum have spent all of their resources getting to the US. The journey is costly, dangerous, and traumatizing. Almost everyone will be starting their life in the United States completely from scratch.