I was referring to those well educated immigrants. They live illegally, so they are not allowed to get any jobs. They all have bachelor and master degrees, and the immigrant laws are limited to make it difficult for them to try to stay legally. That's why they hire immigrant lawyers to fight in order to extend their visas.
As for UK immigrant's situation, You apply for student visa to attend college, and when you finish your college, your student visa ends immediately. You are cut off completely. You're not even allowed to get a job. You must get a sponsor to hire you, so you would stay legally. If you find a sponsor, they must interview a sponsor, and the process takes time, even beyond visa expiration. If a sponsor doesn't provide you sufficient financial in order to support yourself on your own, the USCIS may turn down a sponsor.
Also, It does apply to refugees and asylum immigrants. Let's see how the system work.
Refugees do not have the rights to obtain asylum. However, they do have the rights to claim it. according to the Refugees act of 1980, It violates international law to send a refugee to a dangerous country. If the person requests an appeal, one would not be labeled an "illegal".
In nearly every country that has signatory on the 1951 Convention on Refugees one has the right to claim asylum- but also appeal rejected applications which currently in the United States can take years to be considered. During this appeal process the applicant is NOT in the US illegally and cannot be punished as that would violate the Convention.
Many countries have huge backlogs of asylum cases.
Now, the USCIS made recent major changes, such as increasing the fees to make it difficult for any immigrant (refugee, asylum immigrant,etc) to enter the US. Plus, the US economy is not doing well, it does alleviate the emigration.