An adult plant produces such small fruits. And I would also like to know the name of these small fruits.
This plant is a spider plant, Chlorophytum comosum. The most common variety is variegated with white and green leaves. Wikipedia indicates the seeds can get half an inch long but I have never seen them get that big. They usually dry and drop off when grown indoors.
This plant doesn't even need to set seeds it is so easy to propagate. You can put the plantlets that grow on the end of the inflorescences in soil or water and they will root readily.
Note that this plant is sensitive to chlorine in the water and distilled or rain water will prevent the often seen tip burn