does one year rule apply to only unauthorized stay? the time you stayed in the USA on a valid visa don't count. so a student files an asylum after expiring his I20 is okay even it is after 5 years? please read the following: 

Source : w*w*w*http://immigration.lawyers.com/Immig...al-Asylum.html

Eligibility for Asylum
In order to get asylum in the United States, you must ask for it at a port of entry (such as an airport or border crossing) or file an application within one year of arriving in the United States. Exceptions to the one-year rule might be if conditions in your home country have changed, or if your personal circumstances have changed and those changes affect your eligibility for asylum.The time you spend in the United States with a valid visa isn't counted as part of the one-year period.

You may not be eligible for asylum if you yourself have participated in persecution of others, or if you've "firmly resettled" in a country other than your home country (for example, by obtaining permanent residency in a country other than your home country or the United States). And fear of poverty or random violence isn't of itself enough to qualify you for asylum.

There is no limit on how many people may be granted political asylum each year in the United States.