sed -E, 109 99 bytes

h;s:.:0:g;G;s:0\n(.*): -\1-\n:
:l;s:(.)(.*)-(.)(.*)-(.*):\2-\4-\5+ \3\1\2:;tl
s:. 0* ::g;s:[^ ]* ::

Each line of the input is considered a separate number. Try it online.

Explanation:

h;                                             | copy the original string to the temporary buffer
  s:.:0:g;                                     | substitute all digits with zeroes
          G;                                   | append the original string to the substituted one
            s:0\n(.*): -\1-\n:                 | '0…000\n6…987' -> '0…00 -6…987-\n'
                                               |
:l;                                            | main loop start
   s:(.)(.*)-(.)(.*)-(.*):\2-\4-\5+ \3\1\2:;   | cut the next digit from the number, append with zeroes and add to the back
                                            tl | loop if the substitution hasn`t converged yet
                                               |
s:. 0* ::g;                                    | remove all zero terms
           s:[^ ]* ::                          | remove everything up to the first space

…still plenty of room for optimization.