I could see it as being the total rights to do anything you like for a complete vertical column bordered in the X and Y by the surface plot limits, but to dig outside that area would mean bargaining for mineral rights over an extended area, and some sort of rule something like that of
Ancient Lights applied to overhead constructions.
Perhaps even if subterranean extensions are allowed, extensive digging (or all activity?) within a few Z-levels of the surface might be discouraged. Perhaps this is represented by the cumulative mining-specific noise-effect upon these premises (or even total noise for everything, or a half-n-half compromise to including industry but weighted to allow more extended ability), which has (upon exceeding some threshold or rolling average) the same sort of affect as log-accumulation traditionally does to elvish attitudes towards you.
Any actual disturbance of land outside the permissible area (and/or to surface/ground-floor indoor tiles explicitly part of town or road) would trigger near or actual diplomatic breakdown and could cause hostilities, especially any mysterious "sink-holes" suddenly existing. Any mysterious floods of water or magma coming from above or off of the sub-let land could be taken as breaches of the agreement (...as well, of course, as of the reservoir you so unwisely constructed way up above your segment of town, with such unfortunate architecture as to drain itself out over the neighbours' houses...). If you are allowed to build above other areas (almost certainly this never being allowed in the first place over military/governmental/religious structures such as the walls, keep or temples, though I could see bridges being made to access otherwise unused flat roofs purely for traffic purposes), cave-ins of constructed structures should be severely reprimanded, in accordance with the related building codes that were deemed to be of relevance to your building application and construction permit.
But I could imagine (assuming the rest of the conditions are complied with, and you are assumed to be obeying both the letter and the spirit of the agreement) something like a quick tunnel up into a shop's back-room, when nobody's looking, and the downward stairway covered with a cleverly-hidden hatch... And I wonder if it's possible that some of that shop's stock might 'evaporate' gradually over time...
Could be complex, but... This Is DF!