What would most likely cause the wolf to lie down belly up?

Most likely a wolf would lie down belly up to
show submission

This is a friendly amd submissive gesture because when its doing this its trying to look smaller

It'll also roll over to show a dominant wolf that
it is helpless and not aggressive

In submission to an alpha wolf, another wolf shows his or her belly. The alpha wolf then has the choice to kill, to accept or to run the wolf