i think it depends when he found the new employer, was it within 28 days?
work permit should only take a week or 2 at the most, but as long as the HO have his app, then he shouldn't be an overstayer, depends thou when his employer ap[plied for the permit i think...
not sure about this, not a good idea to quit on a work permit, they should have found another employer first..
If your current employment terminates you:
* Can find another employer willing to sponsor your permit for working in the United Kingdom. The new role must be similar to your current position.
* Must apply for a change of employment permit within 28 days of leaving your current employer.
* and i think apply for Further Leave to Remain (FLR)
maybe when they apply for ILR, they could find they've got a gap and not be able to apply for ILR as soon as they could..
they should seek advice from an immigration advisor
