The word for such a person is "refugee", meaning someone who seeks refuge, often now called an "asylum seeker."
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William Penn
Jews moved to Australiaa in an attempt at escaping persecution, at establishing a new life, and simply because they wanted to.
James Oglethorpe founded the colony of Georgia for the purpose of creating a refuge for England's poor (especially those facing debtor's prisons), as well as Protestant, non-English settlers escaping religious persecution.
Throughout history, many have endured persecution for their beliefs.
William Penn.
It was Maryland.
Maryland
Escaping religious persecution
Escaping religious persecution
Maryland
They were either escaping persecution or looking for a better life.
Someone who leaves a country to live elsewhere in order to achieve their economic desires (as opposed to for non-economic reasons, such as political persecution).
Escaping religious persecution
Most of the first arrivals were people escaping religious persecution.
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Colonists came to America for a variety of reasons, such as escaping religious persecution, overpopulation and poverty.