Bulbils
Special reproductive structures formed by the modification of a vegetative bud or a floral bud are called bulbils.
A bud that would ordinarily have become a branch or a flower instead thickens into a small, self-contained package with a food store of its own. It detaches, falls, and grows into a new plant without ever having been part of a seed.
Examples — pineapple, hemp, air potato.
A flower's place taken by a plant
The interesting case is the floral bud. The plant begins building a flower — the structure for sexual reproduction — and then converts it into a bulbil, which reproduces asexually instead. The same bud position serves either route.
A bulbil is not a bulb
The names are close and the structures are not. A bulbil is a modified bud that detaches from the plant to start a new one. A bulb — the next page — is an underground stem that stays where it is. An onion is a bulb; the air potato's little aerial tubers are bulbils.