OSM doesn't have a specific tag for "unadopted" so adding it would not change anything. There are alternatives (access=private or access=destination) but an editor would expect to see official signs at the entrances to indicate that the land is "private" or to forbid through traffic before mapping it. But that might have minimal effect, if drivers already know about it.
.
Probably more effective would be for the residents to persuade the landowner to install a physical barrier (eg a locked gate) to split the section into two, usually with  a pedestrian and cycle bypass and vehicle access restricted to emergency vehicles.