Abandon/forsake/leave?
Solution 1:
"Abandon" and "Forsake" imply permanence. In your example the people who forsook farms and villages are not coming back. Similarly the owner of an abandoned car doesn't want it any more.
"Leave" can be both permanent ("I left home when I was 18") and temporary ("I leave home every morning at 7:30")
Although "Abandon" and "Forsake" can be applied to both places/things and persons it is more usual to find places/things abandoned and people forsaken. But, of course, your example is an exception to this generalisation. Another exception is children for whom parents cannot be found are abandoned, not forsaken.
Forsaken also has overtones of personal involvement such as in the song "Do not forsake me oh my darling" whilst abandonment is less personal, the thing is just discarded or unwanted. Again a generalisation, not a fixed rule.