You are actually allowed to move outside of Canada while you are waiting for your citizenship processing but in their case, I don't think it would be advisable. You say they have been out for 371 days but actually more because you say they travelled to the US a few times for 10 to 15 days at a time.
If they apply for citizenship and are truthful about the time they were outside Canada, their citizenship application will be delayed, maybe by as much as a year, because it will have to go before a citizenship judge who would want them to explain why they should still get citizenship when they don't meet the residency requirements. If they do that and are at that point not living in Canada any more, I think that will most definitely count against them. Having kept an address in Canada the whole time is irrelevant. They want you to be in Canada, not just keep an address for your mail.
If they are not truthful about the time they were outside Canada, they risk getting caught. Immigration works with the US border, maybe their passports were scanned arriving in the US and passports or PR cards coming back to Canada so it is possible that immigration knows more about their travel dates than they do. It is also possible that they don't. I really do not know the odds of getting caught.
