My immediate thought for this boy was that he was a heavy user of heroin, hence the track marks and heroin users often contract pneumonia and have skin eruptions such as in the PM photo. So at first I thought it was unlikely he was at the Boys Group home as surely drugs wouldn't be available...apparently they were! I did think it an odd place for someone on a trip to be though, but figured maybe he wandered here in a stupor.
But then I saw
@Bit of hope 's post about the tuberculosis hospital and it just seemed so likely to me:
There wasn't much comment about this but I really do think he may have already had a weak system because of tuberculosis or indeed was still suffering. The modern day ME had said she believed he was a drug user due to track marks but in fact the original report said he may have spent time in hospital. Its possible the original ME recognised they weren't actually needle marks from drugs use.
I can't explain why he left in such light clothing why the hospital never reported him missing or what his family was told. Unless perhaps he was already in orphanages and was sent here to heal...literally nobody ever noticed he was missing and the hospital probably just thought he'd left and didnt follow up(after all it's a hospital not a prison).
If he decided to leave and was on foot then after a couple of hours walking and with the cold weather he would have succumbed quickly. Severe pneumonia can kill within hours.
I think he was pretty young and probably didn't have enough maturity to know to wear winter clothes and not go out if he was sick.
As for the crude writing on the trousers; this sounds like nothing more than the scribbling of a bored kid.