There is no published missed approach, but, being you can suggest the contact approach on an IFR flight plan, typically the pilot can see the airport well enough to call off the instrument approach and fly "visually" to the runway. That being said, the aircraft is likely lined up on the runway. If a missed approach becomes required, then the pilot would call ATC back up, mention that they lost contact with the ground, and likely the controller would give them a vector to fly and get established on the missed approach (remember, they can enter back into the IFR system). You can't request a contact approach at an uncontrolled field, it's either a visual approach or an instrument approach (if that airport has one).
Contact approaches aren't used much and I think the AOPA article did a good job summing it up and it's really only to be used within a few miles of the airport. Say the visibility is greater than 3 miles but the ceiling is about 800 ft; since you have the visibility, you could request a contact approach, but not a visual. You're not screwed by requesting a contact approach and the controller isn't going to tell you that they can't do anything for them and that they are on their own. Just call ATC back up if you lose ground contact and let them know and they will likely give you a heading and altitude to fly and then worry about getting you back into the IFR system and onto the missed approach.