Under most cicumstances the pilot will re-direct to another airport. If he may be low on fuel or has no choice but to land he would have to fly in on the last known ILS pattern. Runway lights are designed to be very visible so the pilot should be fine landing a plane with no ILS.

If the ILS systems were to fail during finals to a runway, it would warrant an immediate landing abort under most circumstances. Planes carry enough fuel to travel to one or more alternate airports. If conditions of bad weather were brewing near the primary destination, more fuel is often carried to ensure safe arrival regardless of where they land. I will avoid excessive verbiage about ILS and navigation. Basically, ILS systems consist of a localizer and a glideslope which construct a path to the runway so that the pilot can fly the pattern from looking just at the instruments. Both the localizer and the glideslope are radio navigation aids, so if the signal is lost, this causes a failure of the ILS. Landing in foggy conditions usually warrant a high amount of restriction, ILS and Auto-Pilot Landings aside. There is a whole system of catagories that classify the approach speed, visibility during approach, and what procedures are required by the pilots. For amatuer pilots, or those who are really interested in reading some advanced material about ILS can check out this link to the FAA Instrument Approach Manual. http://www.faa.gov/library/manuals/aviation/instrument_procedures_handbook/media/CH-05.pdf