In ENT episode “Divergence” parts go flying off the ship during warp 5. What would happen to something at that speed without the protection of the field? Would it stay in high speed motion until interacted upon by something else (meteoroids/dust/gravitational fields)? Or would it disintegrate under this kind of speed?
No, we’ve seen that warp field/engine failures will cause the ship to drop to sublight, if they don’t slow to stop, rather than maintaining their current speed.
If it crosses the boundary of the warp field, it might be disintegrated by the resulting stresses, since warp field boundaries can be pretty rough.