Normally if you're lucky the Mailmen will send you another message for another job offering after about 3 days/3 years after you had the old job, that's what happen to me.. I'm not sure that's what just happened to me, but if you keep your Tama Adult for a while he might come again..
I call it the Job Fair, you usually get to change jobs when the mailman gives you a [!] again. For more info on jobs, go to the page called Jobs Descriptions, Info, and Icons
I don't think there's a meaning behind the snake you'll receive in the mail. Just that your happy hearts will all gone, this will happened, too when you received poop in the mail.