I don't know about NY state but here, a project such as that would be regulated by the Government. Neither the property owner nor the contractor would have authority to decide when the cleanup is good enough or too expensive.
Engineering consultants who specialize in contamination remediation would be required to oversee the project while Gvmt inspectors would need to review the process to ensure the task was completed thoroughly and in adherence to regulated standards, regardless of contamination depth. Unlike years past, you can't just bury toxic contamination and have it leak into the aquifer for centuries. Whatever is contaminating the soil will flow downstream to populations which rely on groundwater for life.
I know, when it comes to money, people will attempt to getaway with anything but this contamination is well known and is documented so the project should be under close scrutinty, especially by the Town of Warwick and the people residing around the area.
The test and monitor wells which were mentioned previously, will remain permanently in-place to allow ongoing periodic monitoring of the spread of contamination at various depths.
While this link pertains mostly to petrochemical contamination in ground water, it may help make things clearer: http://oceanworld.tamu.edu/resources/environment-book/groundwaterremediation.html