Can ampicillin resistant bacteria survive penicillin plate?
Short answer: Your assumption is wrong and bacteria, which are resistant to penicillin are are also resistant to ampicillin.

Long answer: There are different classes of antibiotics, which have different mechanisms of action. Penicillin (and also ampicillin) belong to the class of beta-lactam antibiotics which are an irreversible inhibitor of the bacterial transpeptidase, which is needed for the proper formation of the bacterial cell wall.

There is a number of different natural occuring penicillins as well as some which have been generated by modifications of the general structure. The general chemical formula for these is shown below (from the Wikipedia article), the different penicillins differ only in the "-R"-group shown in the molecule (in the upper left):



If you now compare Penicillin G (which occurs naturally and is still used) and ampicillin side-by-side, you will see the the difference is not very big, basically only one amino group:


Penicillin G on the left, Ampicillin on the right.

The difference of this one amino group makes ampicillin more polar and allows it to penetrate the cell wall of some gram negative bacteria (the main action goes against gram positive bacteria).