Sure, that happens. Sometimes airports close because of weather, also. These situations are rare, but you aren’t just routed somewhere you don’t want to go, you tell ATC where you want to go, based upon fuel, company preferences, landing capabilities, weather (or you go into holding and wait). And if they have shut a runway or airport down, it’s irrelevant whether you’re flying IFR or VFR, nobody is getting in. Though I suppose you could declare an emergency and do as you like, but that would have to be a dire situation.