It would depend on how bad the crash was, what aircraft was involved, what kind of airport, and exactly what happened.
For example – if you blow a tire on a Cessna 172, and slide off the runway into the infield at some little grass strip – there will probably be no airport closure at all. Likewise – ground loop a taildragger at such a field and it will also likely result in no closure / no report. (Though you might need to buy silence with a couple of cases of Heineken for the fridge.)
Now if the aircraft in question is an Airbus A-380 and the gear collapsed, causing the aircraft to cartwheel, and there are bodies and smoking chunks of body parts scattered across the entire 10,000 foot runway – well that will be a little harder to keep quiet so the closure will be for awhile – as long as it takes the NTSB and FBI to process, photograph, measure, and otherwise collect every single item in a 2-mile long half-mile wide “Crime Scene”. (Remember it’s a crime scene until it’s ruled accidental)
As for the surface – again can vary widely. Grass strip – fill the divots in with your feet, toss down a handful of grass seed and piss on it. Problem fixed. At the other end of the spectrum – you have run into the frangible stopway area and taken out the airport fence. In which case, some contractor’s mistress is gonna be getting a new Jaguar.