The key word for me here is "willingly."
They're not "willingly" being pushed back into another person's square. They're being shoved back by a Cube in an attack.
I'd say that shove means if they pass, the row 1 people effectively shove the person behind them back as well. Possibly causing them both to fall, as person in row 1 column A collides with person in row 2 column A.
But you can't look at the action at the level of the Row. You must look with more granularity.
I would look at it like this:
- Person in Row 1 Column A (r1cA) passes her save and is forced back five feet. This means the cube can move forward into that square. More on where she goes in a moment.
- Person in Row 2 column B (r2cB) fails his save. He is engulfed and the cube can move forward into that square.
So that's the first piece. The cube has advanced 5 feet, engulfed 1 person and driven 1 person back.
- person r1cA is now in r2cA's square. Oops. r2cB now needs to save or trip. r1cA probably needs to do the same. If they fall, can they still make saves against the engulf? Or just at negatives?
- person in r2cB is threatened and makes his initial save. Pass or fail, doesn't really matter to the Cube; it advances.
At this point, the Cube advances into row 2's range. r2cB can either save of fail; doesn't really matter to this discussion. What matters is how r1cA and r1cB are treated.
As a GM, my play here would be a save against falling for both of them. If they fall, then they're prone and at much greater risk of engulfing. If they pass and still standing, then they are shoved back out of the way.
This old issue of Dragon 124 might help a bit with your question. It was a resource back in the day, though it's not 5e. You asked for any resources including those using old editions--and that article is a treasure trove of useful info you can use.
One particular bit on page 57 of the issue:
As to their digestive fluids these are produced and held in movable,
elastic cavities or bubbles within an athcoids body. When prey is
engulfed by a cube, one or more of these mobile bubbles are shifted
into contact with the prey. Such fluid has no effect on metal of any
sort, and, as we have all heard, metal objects are held for a time
within the creature, then expelled through its skin; but the fluid has
devastating effects on flesh and cellulose.
I would posit, based on this that the cavities or bubbles are maintained within the creature, and that upon death, they deflate and the creature loses cohesion.
It's DM call on if the acid of the cube still has an effect after it's "killed." What I have done, as it loses hit points is allow it to puddle in the hall around the PCs. For about a round it remains acidic--but that's a DM call there. As they take away the hit points from the creature, it does naturally move toward warmth vibration and sound, so even if it is a bit shorter, it will try to block their way.
Once it's dead, all that mass has to go somewhere, and I work it like a gel-filled balloon that's been popped. But--you can work it the way you did, ruling that it maintains cohesion for up to an hour after death or more, or less, that's your call as the DM.
I have also had some fun with PCs once they have defeated the creature by having the gel start to coalesce again--remaining bits into baby cubes. The PCs were so freaked out by it shifting to come together again that they simply ran away, despite the fact that the baby cubes would have moved away from them as they are now too big to eat. That isn't at all canon--I just like throwing something their way they haven't seen.
Not all cubes are going to be the same--I use the MM as a jumping off point and assume that some creatures in an isolated dungeon might have developed slightly differently. It also keeps my players from metagaming too much--if they are of a particular level, they expect specific creatures in their range, which is annoying, because they will try to use out of game knowledge to fight said creatures.
Best Answer
It gets to keep engulfing.
Here's the relevant part of the Gelatinous Cube's Engulf action:
So what doesn't happen is that it uses its action to try to engulf you, and then can't do it again this turn.
What happens is that it gets to move the entire 15 feet, and attempts to engulf anyone in its path. If it starts its turn within 10 feet of you, and there's no space to dodge out of its path, it can force you to make multiple Dex saves to keep running away.
This is its hunting strategy. The Cube is an ambush predator. It can't catch victims who have any space to run; it needs you to get as close as possible before it moves. The closer you are, the more Dex saves you have to make to escape. It has a few tools to support that strategy:
The best case for the Cube is that some sucker blunders right into it. The victim will have to make one save with disadvantage immediately, and then be surprised, which gives the Cube another three tries to engulf them on its turn. So they have to pass five Dex saves back to back. This isn't even an unlikely scenario if it can hide in a dark spot that's accessible to surface-dwellers. If it's in total darkness, it may well be impossible to detect.