He really needs to stay at that job until his extension is approved. They do conduct random checks and contact employers.
I don't think they are all random, not since UKVI was given access to the other departments records.
HMRC went onto a new system called Real Time in the tax year 2013/4, where the employer must inform HMRC each time they pay an employer, instead of once a year. Therefore UKVI and the benefits offices can see where they are working/earn what they claim they are. All it takes is a quick call to the employer after that to check/tell the employer they have no right to work. Sweeps of the systems can be done at anytime.
Judging by the floods of posts every now and again from those who have had their ILR or BC removed for deception, having held that for years already, I guess UKVI sweep with any new shared information too. Some wouldn't have been refused with the correct information anyway, but using deception is serious. This is why I don't think these calls are all random, as they don't need to be now. You don't see these type of posts on uk-yankee as people on here are always correctly advised to be honest in their applications/use a good solicitor for any problems there might be on their application.