Floroid, 69 bytes

a,b=L.J c=1 NZ(a)!=1:z(a);a=a[:-1] z(a) NZ(a)!=Z(b):c+=1;a=b[:c];z(a) 

It's a start. Takes the input from STDIN.

Testcases

Input: Test Testing Output: Test Tes Te T Te Tes Test Testi Testin Testing Input: O O Output: O