Let $M$ be a smooth manifold, $N\subset M$ be a smooth closed hypersurface, and $X$ be a smooth nowhere-zero vector field on $M$. I would like to learn what is known about the following 

**Question.** When can $N$ be moved by an isotopy to be nowhere-tangent to $X$? 

In particular, are there invariants that can be used to imply a negative answer even when the embedding $N\hookrightarrow M$ can be homotoped (not isotoped) to a smooth embedding nowhere-tangent to $X$?