Problem with Op amp and zener diode circuit
You're correct.  A useful concept here is a virtual ground...when connected in a negative feedback situation, the output does whatever it can to make the negative input look exactly like the positive one.  Since the positive input is grounded (and I'm assuming that's within its common mode voltage range) the output will increase with decreasing Vin until it reaches the zener breakdown, after which it can supply all the current it needs with a voltage of 2V.