The ones that survive a round spread their health amongst all of them in a single wave.

I want to say it gets distributed over all of them. But I'm not fully certain there because I recall waving being necessary for SGs.

Because SG's fill the frontline spot, the weakest units get picked first. So if you send any group - the weakest in the group will be used (in this case your dying SG). This is the reason why you wave - you basically are removing the weak units when you recall and sending in a fresh new uninjured batch. If you send a second group - the weakest units of any that are fighting will still be picked first, so make sure to always try to send in sets so you can recall the injured units. When they arrive back in the orgin city (1 hour + travel time) you sent from their HP is revived and you can send them in fresh again.

This is also why if you don't have unit upgrades or forge sending in frontline units to a battle is a bad idea. (and why you should instead opt to send swords or spears so that you don't scatter but can also contribute).