Had this situation described...need expert advice:
A1 dribbling in A's backcourt up the sideline. B1 and B2 apply pressure, forcing A1 toward the division line/sideline corner. Just before becoming completely trapped, A1 pushes/passes the ball through the defenders, steps OOB, runs around defenders to frontcourt, steps back IB, grabs the ball.

Violation?

Due to the fact that A1 left the court voluntarily I would say it is a violation.

Another question is a modification of the above scenario, what if A1 leaves the court involuntarily?

Thanks in advance for the comments.

A1 gained a clear advantage by going OOB -- violation.

Yes.
How do you mean "involuntarily"? Was A1 pushed out? Was there a possible foul by B? Or did they just bounce off one of the defenders and fall OOB? And how did they get up, get back inbounds, and still beat B to the ball? This one may be a little harder to determine, but it doesn't sound like a clear violation on the surface.