I'm going to take a wild stab at this with my limited knowledge and hope that I make sense.
Have you ever seen light distorted around the edges of a black hole when it is viewed from a certain vantage point? When an incredibly dense object bends the fabric of space, it creates an immense gravitational pull around it that essentially sucks in every particle of anything ever, and all those particles become a part of the incredibly dense object at the "bottom" of this black hole. It destroys everything nearby because it creates this pull.
When we warp travel, however, we don't alter any gravitational fields. We have theoretically harnessed the power to bend space (possibly aided by antimatter as in Star Trek) like a black hole might. We can jump across large distances by wrinkling up space and moving across these divots. Before warping, space captains often plan their trajectory to avoid hitting anything that might be in the "cracks" of the divots they hop across. We have to assume that the objects that are moving within the fabric of space are at least somewhat fixed in their positions when we bend space. They are not affected by the warp, but they do not necessarily "ignore" it, or else we would just smack into unmoved objects.
Imagine a drawing on a piece of paper. We crumple the paper, but the drawing remains relatively intact on the paper. This is theoretically how objects in space would behave if we warped space without changing gravitational fields.
I really hope this doesn't sound ridiculous.