suggest that before you return from Singapore you have made a reservation for your flight to VN - print out that confirmation - don't offer it until and if asked when you return. I entered in Jan for 2 weeks, then May for 3 weeks and then early June for 5+ weeks when I left for the purpose of filing and obtaining my DTV visa - I was not questioned at all during any entry. When I returned with the DTV visa (approved and issued) I had a print out with me and presented it when I got to the agent - no problem at all Once you have it you need to present the physical copy each time you enter - I asked the agent this question directly and that is what he confirmed. You should be fine - but do be sure you have booked your flight to VN before you come back from SIA - Air Asia is a good option and inexpensive.
he should call his embassy and find out directly from them - it will not be the first time they have gotten and inquiry like this - and they will know what to do - way better than random people here. My only other input is he should consider leaving asap - overstay is taken seriously and can have ramifications beyond a fine - including refusal to allow return for a period of time. He should leave and sort it out re the new passport elsewhere - if he has already overstayed 2 weeks he needs to leave - pay a fine and beg forgiveness
ExcellentJackfruit8779 sorry not willing to share more details with an anonymized poster. I did use an agency so you may wish to do so and get guidance tailored to your situation