In order to travel to the US most people need to apply for a Non-Immigration Visa to enter legally. Under the Visa Waiver Program there are 38 countries that do not need to apply for a visa if their trip is less than 90 days.
If the property owner validly disposes of the property by will and the property has a valid mortgage, then the person that inherits the property will hold a valid title to the property and the holder of the mortgage will retain a lien on the property.
The Truth about Approval Rates of Asylum Petitions in The United States
The United States receives on average over 20,000 Asylum petitions a year; of those Asylum petitions received the vast majority are denied every year due to petitioners inability to prove they meet the United States requirements.