So, the scope can continue to function indefinitely, it just can't manoeuvre. Maybe the question should be, what is the most interesting part of space to point at before the thrusters die?
The disappointing follow-up question being, "And how would you hold that aim point without fuel and reaction wheels?"
Unfortunately, Kepler is already on a reduced-function mission, the K2 or Second Light mission. The K2 mission came about because of the failure of 2 of 4 reaction wheels on Kepler (in 2012 and 2013, respectively). K2 depends on some clever solar sailing, at least in the sense of preventing light pressure from disturbing Kepler's aim while it makes months-long "viewing campaigns" of certain areas of the sky.
Under the K2 mission, Kepler's view changes through the year due to its rotational inertia, light pressure, and need to avoid letting sunlight directly down its telescopic throat. This period of reduced function still depends on the reaction wheels and fuel as Kepler must be periodically rotated. (See link above for a diagram.) Lose another wheel or run out of gas and you lose aiming control, at least partly due to the inability to fight sunlight pressure.
So, when you aim Kepler into the Great Beyond for its hypothetical fuel-free K3 mission, it's not going to hold that aim for long. Not even months.
Biting the hand that feeds IT
