Can blocks of ice escape from the Oort cloud and away from the solar system forever?
The Oort cloud objects are only very loosely bound to the Sun. That is, their total energy (kinetic plus gravitational potential) is only just negative.
That means you only need a slightly positive perturbation to make those objects "fall out" of the Solar System. Conversely, a small negtive perturbation would cause them to fall inwards - and can give us long period comets.
What could cause these perturbations? The tidal field of other passing stars or structures (spiral arms, molecular clouds) within the Galaxy. Remember that the influence of these will not be felt immediately because the orbital periods of Oort clouds objects are at least thousands, if not millions of years.
As some of the Oort cloud objects leave the Solar System then the cloud as a whole must lose some mass. The Sun will also capture some objects, as it moves through the Galaxy, but this is unlikely to be a symmetric process.