There has been a study that indicates the entire side of that mountain could slide into the Atlantic. The amount of earth and the resulting displacement could cause a major tsunami along the East coast of the US, especially major metropolitan areas like NYC, seeing as it sits at the mouth of the Hudson, which is, if I remember correctly, another active fault line.
Wrong Canary Island. That island is La Palma. This is Hierro.
There is a possibility that a seismic disturbance could cause that fault line to let go, dropping half the island into the ocean and generating a large tsunami.
The tsunami science generalhy believes the threat of a massive tsunami on the East Coast of the US from La Palma is BS.
The promotor of the La Palma landslide/giant East Coast tsunami idea is a handful of scientists, lead by one, Simon Day, who I think has let all his appearances on crappy cable science disaster documentaries go to his head.
Unfortunately said crappy documentaries do not give a balanced view, because they're all about neat-o computer animations of a 150 foot wave sweeping over the Statue of Liberty.
Lesson is: don't get your science education from cable TV.