It cannot. The event horizon by definition prevents mass and energy from leaving (ignoring the exception of Hawking radiation here). I'm assuming your "black hole droplet" would be a tiny black hole? But if you could remove a little chunk from the black hole then you've effectively taken mass out of it, which is impossible.

It is even the case that once two black holes have overlapping event horizons (so they "touch" in a way) they can't stop touching. So two black holes can zip past one another at a small distance, but if they high-five they can't stop merging.