It's ESSENTIAL to keep taking your insulin when poorly, so that was indeed very poor and dangerous advice

DKA does strike very rapidly. What happens is that the body can't process the glucose being supplied from food properly so it turns to burning body fat and tissue. Ketones (the 'K' in DKA) are a by-product of burning this fat, and without sufficient insulin they build up in the bloodstream turning it acidic (the 'A' in DKA) and causing all the problems

He should get a blood glucose monitor that can also monitor for blood ketones - you can use pee sticks, but these are very unreliable and only show the situation from a couple of hours earlier - blood ketones test strips will show the levels as they are now. The Freestyle Optium from Abbott takes blood ketone strips as well as blood glucose strips (there are other meters, but can't remember them offhand).
You might like to read
Type 2 Sick Day Rules to give you a better idea what to do if he is ill again. He should, however, speak to his nurse or doctor about the insulin he uses and how he should adjust it if poorly - people can have very different requirements, so the doses suggested on that page may not be suitable for him.
He is still Type 2, but because he is on insulin he is still prone to DKA - a Type 2 who is not on insulin will be less likely to suffer from it as they still have some insulin production of their own. Hope he is home soon and feeling much better. When he is better, give him a good talking to about taking his insulin
😉 I also hope he is able to find another job very soon
🙂 Let us know how he goes on, or if you have any other questions
🙂