If the dirt/soil is bone dry directly beneath the grass, then there's not much you can do other than go somewhere else, or focus on shallow targets and use other techniques to extract the coin. A shallow coin can easily be pinpointed prior to digging with a handheld pinpointer and then removed with minimal disturbance of the grass/soil.
So, one takeaway is to only dig large plugs when you need to go deeper than what your pinpointer can detect. Cut a slit or a very small plug. If the grass dies it will be unnoticeable.
Whether the ground is dry or not, a 360 degree can still kill the ground cover depending on what it is. Some ground covers are creeping and usually won't survive just on the small roots put down as they grow sideways. A 360 degree plug will literally cut that plant off on all sides and what's left in the middle will die. A two sided V cut flap for medium depth targets, or a 3 sided square flap for deeper targets, will keep the ground cover attached/uncut on at least one or two sides. That increases it's chance of survival.
If it's turf grass, a 360 cut will also kill it if you don't cut the plug deep enough, or if you do a cone shape plug. In either case, your cutting the roots off. Just cutting deep enough to peel back a flap of grass and then digging out the hole will probably kill the ground cover.
To protect the roots (and the target), cut plug walls straight down past the roots. Ideally, your plug should have dirt attached to it with roots inside.
For similar reason, don't cut plugs in a cone shape unless there's a good reason. You not only risk stabbing the target, you cut roots short around the perimeter. Plus, you'll have to remove a bunch more dirt unless your pinpointing was spot on.
Its counter intuitive, but the pristine yards with thick turf grass are the easiest to keep alive because of the deep vertical root development. Pop out the shallow targets, and for the larger plugs either cut two sided V flaps (medium depth) or 3 sided square flap plugs (deep) all with straight walls. Go a few inches deep in the first cut to protect the roots. If the coin is in the plug, then just extract it from below and don't tear the roots up more than necessary.
