Do many employers advertise jobs that have been taken?

Wintermute

It's very common in the public sector, my Mum's high up in a public sector organisation and has had to apply for her own job twice relatively recently due to certain policies, she's also applied for jobs within other public sector organisations despite pretty much knowing for certain who's going to get the job before it was even advertised, in the public sector at least it's part of the system. In the private sector they don't need to advertise anything at all, as far as I know my previous job was never formally advertised.