I don't know what operation they are running, but I work 100% from home for years as contractor under same conditions as him (heck even my name is Peter), was never hired for this position in person, I don't think I even did any interview or video chat, just passed the test (though I work on stuff position in person many years ago, since then there are no people who met me in person working there), but when I communicate with different PMs they have all their Chinese work landline numbers in signature and they have clearly my number in system, since occasionally (maybe 5 times a year?) when I don't respond quick enough to their emails someone dares to call me from Chinese number in broken English.
So even if I had locked computer/phone (which I don't have) and wife couldn't just reply any email (several dozens per day) or see phone number in email I can only imagine it would take them only few hours to realize I'm not answering and my phone would start ringing like crazy.
Btw we never talk personal life, they can only learn about it, if I explain why I won't be available in certain hours because I'm going to hospital or we just politely wish each other nice holidays, all emails are strictly work, we don't even chat and during occasional video training I never switch on my camera.
So considering all of this what kind of company is this they don't have his phone number to call? And how can they not notice he is not answering his emails and not just call to check on him? Unless he is not that important part of team they won't notice he is missing until his wife let them know.