You poor man, you must be so worried. I used to have cats, I love 'em. Having said that, one of them regularly used to do the off for a couple of days and turn up none the worse for it – apart from being starving!
I'm not sure what to say, I can't put myself in your position because firstly dogs don't go walkabout like cats and second, if Missy was locked in somewhere, she would make so much racket that there would be no doubt, but in that unlikely event, yes, I would break in to someone's house (and get totally stressed out about it) and face the consequences later.
However, as posted above, surely someone has a key, or a phone number or email address for this person? Do you know the name? Can you look up and ring the home number? Some people check their messages remotely. Also, there are mobile phone directories, maybe you could look up the name?
Good luck.