ON AN AIR TAXI FLT TO A PRIVATELY OWNED, PUBLIC USE ARPT, THE TRANSPORT CATEGORY ACFT TOUCHED DOWN HARD, 7 FT BEYOND THE BEGINNING OF THE 2500-FT-LONG RWY. THE HARD SURFACED RWY'S STRENGTH WAS INADEQUATE TO SUPPORT THE ACFT'S 9500 LB LDG WEIGHT & THE ACFT'S LEFT WHEEL PENETRATED THROUGH THE 3/8 INCH THICK RWY SURFACE CREATING A 4 INCH DEEP HOLE. AS THE ACFT CONTINUED ITS LDG ROLLOUT THE LEFT LDG GEAR BROKE & SEPARATED FROM THE ACFT. THE ACFT VEERED OFF THE SIDE OF THE RWY & COLLIDED WITH A SHALLOW DIRT EMBANKMENT. THE ARPT WAS BEING OPERATED UNDER A STATE OF CA PERMIT, ISSUED IN THE BASIC UTILITY 1 CLASS & IT WAS DESIGNED FOR LIGHT ACFT HAVING A GROSS WEIGHT OF 6000 LBS OR UNDER. THIS INFORMATION WAS NOT DISSEMINATED BY THE FAA IN EITHER ITS AIRPORT/FACILITY DIRECTORY OR ON THE CURRENT AIRPORT MASTER RECORD. THE PIC'S REQUIRED FIRST CLASS AIRMAN MEDICAL CERTIFICATE HAD EXPIRED. THE RWY LENGTH WAS SHORTER THAN REQUIRED FOR THE AIR TAXI OPERATION.