Usually, asylum applicants find themselves without the chance for an approval if the conditions in their countries improve. For example, those harmed by the Shining Path guerrillas in Peru might have a very difficult time obtaining asylum because that terrorist group is no longer as pervasive as it once was.
Fortunately, if foreign nationals suffered harm in the past, there are TWO ways that they still may be eligible for protection in the United States. This was highlighted by a recent unpublished Board of Immigration Appeals case about a Romanian citizen. The first way is if the foreign national demonstrates "compelling reasons" for being unwilling to return to the home country. This is due to the severity of the past harm suffered; the foreign national may have depression, anxiety and emotional suffering about returning.
The other way to obtain asylum, even if the situation in the homeland has improved, is if there is a reasonable possibility that the foreign national will suffer "other serious harm" if returned. Note, there does not have to be a likelihood of harm, just a reasonable possibility. Also importantly, the harm does not have to be based on a protected ground. Reports that the general population suffers from poverty or civil strife would be sufficient.
For the best shot at a life in the U.S., talk to an immigration attorney about your personal circumstances.