Can I Get A Contactor Without Connecting the Neutral Side? (A2)

If you have disconnected the final wire attached to A2 on the contactor coil, it cannot be energizing. Energizing 1/2 of a circuit is not an energized circuit.

So there are only 2 possibilities that I can think of:

1. You are mistaken in your observation that A2 is disconnected. As SolarEagle suggested, you may have a set of welded contacts somewhere and you THINK you are opening the circuit by disconnecting it somewhere else, but in fact it is not disconnected. A simple volt meter check across A1 and A2 can eliminate that possibility.
2. You are disconnecting the actual final wire at the A2 terminal of the coil, yet it still remains engaged. In that case, the only possibility that remains is that the coil windings have become grounded inside of the coil, and your A2 circuit is part of a grounded Neutral, so an internal path to ground makes the circuit valid for the coil power. It may be less than full voltage because of where in the coil windings it grounded, but it would/could be just enough to pull in the armature.

Additionally some brands of contactors have TWO A2 terminals and the coil could be getting back-fed through a circuit connected through the second A2 terminal.