Original pilgrims that landed on America isolated since landing?

There was no group of the original Pilgrims who got "isolated since landing." The original Pilgrims remained in contact with Europe and later with other British settlers in America; their genealogy is well-documented and there is a large organization of their descendants (the Mayflower Society) today.

You must have been watching some wacko conspiracy-theory TV show, or a fictional movie.

You're not thinking of Ocracoke are you? The residents of that island supposedly spoke 18th century English until well into the 20th century when all the tourists came to hear them speak 18th century English.