This is possibly off-topic here - please redirect me if necessary
I am looking for the name of a type of word where you can continually remove one letter from the start or end of the word, until there is just one letter left, and every intermediate word is a valid word in the English language.
brandy is such a word, because after each letter is removed below, we get another word:
brandy brand bran ran an a
What is the name for words with this property?
I'm new on ELU.SE; I can probably do with some help with tagging this question correctly.