My husband and I sold our first home 3 years ago to a couple who are now claiming that there is faulty wiring in the basement. They refused an inspection when we closed, and now 3 years later say they want us to pay for the new wiring or they are going to take us to court. Can they legally do this?

Anyone can sue anyone for anything but that does not mean they will prevail. You house sold "as is" and unless you intentionally tried to defraud them you owe nothing. Here is an example of intnetional friaud. I bought a home that had a large set of wooden shelving screwed into the wall. When I removed the shelving I found a rather large crack in the foundation that had been patched with caulk. The seller ended up paying $900 to have the crack repaired professionally.