Is this possible, even if the player is not online/alive anymore?
(I'm beginner with C#)

            var entities = BaseNetworkable.serverEntities.Where(e => e?.name != null && e.name.Contains("skull_fire_pit")).Cast<BaseEntity>().ToList();
...           
            foreach (var entity in entities)
            {
                if (!entity.GetBuildingPrivilege())
                {
                    entity.Kill(BaseNetworkable.DestroyMode.Gib);
                    continue;
                }
...

                BasePlayer owner = BasePlayer.FindByID(entity.OwnerID);
                if (BasePlayer.FindByID(entity.OwnerID))
                    owner = BasePlayer.FindByID(entity.OwnerID);
                else if (BasePlayer.FindSleeping(entity.OwnerID))
                    owner = BasePlayer.FindSleeping(entity.OwnerID);

                if (owner == null)
                {
                    entity.Kill(BaseNetworkable.DestroyMode.Gib);
                    continue;
                }​

In indisght covalence.Players is more suitable, but it would require a lot of change to other parts of the plugin

Why do you need to save BasePlayer? Technically, you can do that. But I don't understand why

No, you cannot save an entire BasePlayer object in a .json data file. You can save the data (granted that it can convert to text) that each part of that object contains, but not the entire object.

Bad design choice.

A BasePlayer variable is used throughout the plugin, it initialize normally if the player is either online/offline and sleeping. But if he's dead and offline, findbyid/findsleeping is null. Figured save/load could be a way, also an oppurtunity to learn more.

Base player is a class. Its not like your created class, its dynamic and different. You CANT. If you need help - accounce your current problem why you want to save BasePlayer - we will help.