What happens when a Black Hole slows down?

I’ve often read/heard the description of a Black Hole as

The remaining bulk, still several times more massive than the Sun, collapses into a single point of infinite density, called a singularity

Often with some variation of “from which nothing can escape, even light”.

I was reading a reader comment in New Scientist asking “What about gravitons”, which made me think.

Presumably an object being pulled towards a black hole exerts drag on the black hole: the moon slows the earth by about 1.5ms a century (ref).

Black Holes are actually categorized as rotating and non-rotating, and the two kinds have very different properties. But what happens when one slows down and stops rotating? And can a large enough mass interacting with a non-rotating, can the drag cause it to being rotating?