What you see in the picture is the main stack (background, green) and two other pipes joining it . You can also see two perforated straps that were used to support the pipe just below the join with the pipe that goes to the left (that goes to the upstairs toilet, blue on the picture)
I am closing the ceiling back and I think that I removed some sort of pipe (red in the picture) that was there connecting the two perforated straps, they both have loops and screws to tighten those loops
I want to put that piece of pipe back or if you have a better solution please suggest it. Can that pipe be any material or it must be a certain type (I think it was copper) I know that as with aluminum if you leave copper in contact with certain metals you could have issues
Update: how about riser clamps ? Maybe I should add one when I open the wall in the upstairs bathroom. The reason why I am worried about this is because it seems that a long time ago someone cut the copper 4" stack at the entry point in the basement slab and replaced that with ABS so now the entire stack sits on a rubber connector that makes the transition from copper to ABS ...it seems OK but I think it is a little bit compressed and if it is not lifted a bit it will end up cracking some time in the future. It might never happen and there might be some support, that I am not able to see now, with a raiser clamp in the ground level bathroom wall that is above.