Name for words that may be split into two words, regardless of space placement [closed]

Is there a name for a word that becomes two words regardless of space placement?

A trivial example would be the word "aa" which becomes the two orthographic (but identical) words "a" and "a" when cleaved in the middle.

Another example is the word "aba" which becomes the words "a" and "ba" when split after the first character, and "ab" and "a" when split after the second character.

The answer is no, as far as I know, there is no such word. The nearest is the palindrome, being a word, phrase or sentence that reads the same left to right and right to left:"able was I ere I saw Elba."; or "Madam, I'm Adam." These are the best known of these. They are only interesting enough to acquire a special word as a mild curiosity, difficult to make up but of no literary interest.

Come to think of it, "Madam" is not only a palindrome but one of your a ... what shall we call it?

schizonyms might do; schizo (σχίζω) is the Greek word meaning ‘I split’ as in schism. I cannot imagine a schizonymic poem being written. Perhaps it could be done. Would a reader understand it? Now there is a thought. It might be used for some sort of schizonymic code, to be decoded by picking out the schizonyms and fitting them together.

Surely not.

I am concluding 'no' after a thorough search and collecting the answers provided here.

I did find some interesting names for unique words including ambigrams and antigrams.

I wrote a program, and I found that there are only 13 such words in the English language, so @Hot Lick's guess was almost exactly right.

Here are the words: 

AA
ABA
AHA
AHI
AI
ALA
AMA
AMI
ANA
ANANA
ITA
I
A