"Submissive behavior" means someone displaying actions or attitudes that show they are obedient, passive, or easily controlled by others. Full definition
The pup would scream horribly, fling himself on his back and pee on himself in the ultimate show of submissive behavior. (professorshouse.com)
A frightened dog may try to escape, may show submissive behaviors (avoidance of eye contact, submissive urinating, rolling over to expose his belly), or he may freeze and remain immobile. (nevadahumanesociety.org)
In this case, the dog gave ground and made himself «invisible,» which is submissive behavior in dog society. (animals.howstuffworks.com)