In my 1st Edition Rules, section 4.3 Supply from the middle of the first paragraph to the end of the second:
Any units which are not in supply, and remain so at their end of their turn, are eliminated and returned to their Force Pool. ....
Supply has no effect on Combat but does affect Movement. Ground units out of supply cannot move, regardless of the Option or Phase employed. Naval and Air units are always considered supplied. Airborne (4.7) units or armor units conducting Exploitation (4.5.3) are considered in supply during and one turn after they conduct their air drops or Exploitation.
Beneath that, in the caption of the diagram illustrating an Out-of-Supply situation on the Eastern Front, it says:
The Black player has just finished his move, leaving all the Red units isolated and out of supply except for the 10th infantry which ....
The 4th Edition Rules below agree, though in a somewhat more verbose and comprehensive fashion, so I am lead to believe that the rule has not changed over the editions:
27.43 Unsupplied units are eliminated if still unsupplied at the end of their player turn. This is so even if they were in supply at some intermediate point of their turn. Elimination occurs at the end of the player turn; units are lost after unit construction, therefore units lost from lack of supply cannot be reconstructed during the turn of their loss.