This strange critter is called a Solenodon. It is among the oldest mammals on earth.
These evolved around 76 million years ago during the age of dinosaurs.
They were wiped out long ago everywhere except on a few islands they had migrated to
where very few other animals lived and no predotors hunted them.
In Cuba, Haiti and the Dominican Republic, they are still found today though rare if you know where to look.
South side of Dominican Republic