Batteries wired in series electrically operate as one battery, as the end cell of one battery is joined to the end cell of another via the series wire between the batteries.
It’s not the best to connect a discharged battery to a charged battery in series and attempt to charge it in a set. This could cook the good battery because the discharged battery will draw a very high charging current that must pass through the good battery.
Batteries in series should (shall per code) be from the same manufacturing lot, and should have the same state of charge when they’re installed. For us, batteries come in cases of 8-10 so that’s typically never a problem. This way, that battery set is always charged and discharged at the same time with the same current (series circuits, current is the same at all points). 80% of the time, these batteries will also fail at the same time. Now, if you mix, say a Werker from 2010 with an Ultratech from 2009, you have two batteries that have different chemical compositions. It won’t cause any noticable harm, but one could have a higher sulfation buildup than the other, etc. Not a big deal for the applications of the panels on this site, but I’d replace them on a service call.
Personally, I would get that dead battery charged before putting it in the panel. If it’s less than 1 VDC you have some serious trouble, it’s very, very, very bad for a battery to be that low (it can damage the lead plates by a sulfation buildup, that reduces the battery’s current). I carry a 500 mA trickle charger that I got from a local battery shop. It’s great for that kind of thing and only cost about $20. Also, if it’s been sitting that low for more than a few days, irreversible battery damage could have already been done. These alarm batteries are cheap, I won’t lie. I see some fail, crack, leak, etc sometimes 2-3 years after installing, they all bear that same sentence on them, “made in China”.
I live not far from the Yuasa battery plant in Reading, PA. I’ve seen those Yuasa batteries go 10 years and still pass load testing. No lie, I’ve seen Yuasa batteries split and crack open and they still pass load testing. Off topic, but domestic manufacturing quality shows.