According to The Star Trek: The Next Generation Technical Manual, Chapter 5 - Warp Propulsion Systems, page 54:
The space-time continuum distortion based propulsive effect of a warp field is created by nesting several layers of warp field energy together, with each new layer exerting force against its outermost neighbour. The cumulative effect of this force results in the massive subspace field distortion that allows the ship to reach faster than light speeds.
A great amount of force is exerted on the Warp Energy Field when travelling at Warp speed. The faster the Warp Factor, the greater the force exerted and the more strain put on the system. In addition, the more you push a Warp Core, the less stable the field becomes. If the Warp Core were to completely fail whilst travelling at these speeds, the distortion field would collapse and the ship would be subject to all of the aforementioned forces, ripping the hull apart.
Similarly, it was mentioned in the episode "Deja Q" that an object not entirely encompassed by the forward end of the warp field may be destroyed by a subspace compression anomaly as it passed through it. This suggests that the warp distortion field is a critical factor in maintaining structural integrity whilst being subjected to extreme force.