Hi, yes; these people are often referred to as [United Empire] Loyalists. Not discouraging more contributions here, but fyi, there have been a few great threads on their post-American Revolution experience.
These posts are all archived by now, so if you have follow-up questions for any of the users, just post here and tag their username to notify them.
Loyalist emigration from the newly formed United States featuring /u/Magneto88
After the American revolution, what was it like for loyalists and people that didn't go one way or the other? featuring /u/shazbot14
Was there anything like a Reign of Terror during the American Revolution? featuring /u/Prufrock451
What happened to property owned by Loyalists after the independence of the USA from GB? featuring /u/TRB1783
What Would Life Be Like For a Loyalist Before, During and After The American Revolution? featuring /u/lordkettering and /u/TRB1783
How were empire loyalists treated in the US following the British defeat in the American war of independence? featuring /u/plusroyaliste
How were Loyalists treated after the end of the American Revolution? /u/GeneralLeeBlount on North Carolina