Welcome to PB fellow Miserian.

Research "karst topography".

You might be able to drain it and apply a new clay liner with some success, but there are no guarantees that it will hold.
Installing a synthetic liner might be a better bet.

I know of a few problem ponds located on the karst near Rock Bridge State Park south of Columbia.
One in particular is noted for dumping its contents into the cave system every ten or twelve years.