If you have been granted permission to live in the United States as an asylee, you may take the next step and apply for a green card (lawful permanent residence) one year later. That puts you on the path to U.S. citizenship. You are not required to apply immediately after the year is up—there is no time limit—but there are good reasons to get your application in as soon as you are able.
The main reason is that the source or danger of persecution sometimes disappears after an asylee has already been granted status but before he or she has obtained U.S. citizenship. Even if you still feel unsafe returning to your country, the supposed end of a civil war or something similar can lead the U.S. government to think differently. The question then becomes whether the person will be allowed to continue living in the U.S. under these changed circumstances.
If you received asylum in the United States, the law requires that you continue to meet the legal definition of a refugee in order to keep your status. That's why you are at risk of losing your status on the basis of changed circumstances, including changed country conditions.
What if, for instance, the government that persecuted you is overthrown, the guerrillas and the army sign a peace accord, or the law under which you are persecuted is taken off the books? The U.S. government could decide that it's now safe for you to return, and take steps to cancel your asylee status.
Even in such a case, the U.S. government will not rely solely on changed country conditions in deciding whether to terminate your status. You might still keep your asylee status if, for example, the persecution for which you were granted asylum was especially severe.
In contrast, if conditions in your home country have improved significantly since you became an asylee and you have voluntarily returned to your country or obtained a passport or other benefit from there, then you are more likely to lose your asylee status in the United States.
Information about improved conditions in your country could come to the U.S. government's attention when, for example, you request admission at a U.S. border or entry point upon return from a trip.
It could also surface when (one year or more after obtaining asylee status) you apply for permanent residence. So, there is a risk to applying for a green card if conditions in your country have already improved. That's why it's often wise to apply for the green card even before signs of improvement appear, if possible!
In any case, your asylee status would not be terminated out of the blue. You should expect to first receive either a letter informing you of USCIS's intent to terminate your status (and giving you 30 days notice of an interview in which you'll be expected to show why your status should not be terminated), or a Notice to Appear in immigration court (an NTA)—depending on which of these two government agencies granted the asylum.
Applying for permanent residence as soon as you are eligible is the first step toward reducing the likelihood and the impact of U.S. government inquiries into changed conditions in your country.
Although this application could trigger a basic inquiry into your status, that inquiry is unlikely to focus on changed country conditions. Moreover, if the circumstances are already such that changed conditions could affect your asylum grant, then your status is likely to become only more vulnerable over time.
However, even after you have become a permanent resident, the issue of changed country conditions could surface if you subsequently find yourself in removal proceedings on other grounds, such as having committed a serious crime, or if you travel back to your home country. Therefore, the surest way to permanently avoid the impact of changed country conditions would be to eventually apply for U.S. citizenship. And to do that, you must first become a lawful permanent resident, and hold that status for at least four years following your one-year as an asylee.
Given the complexity of these considerations, consider seeking the advice of a lawyer regarding the details of your case.