Why in Overlap Save Method in DSP output length comes out to be same as input length?
Your "Case 2" convolution using overlap method processing really comes out to 3L + M - 1 with M - 1 (or more) points discarded.   And another 2(M - 1) points computed and summed into the middle of those 3L points that you see.

The key concept is in the word "overlap".

So no extra points are appearing because they're always somewhere (summed or trashed).