I'm worried my ponytail palm is dying because its leaves are falling off and there's black stuff on the top. Can you tell me if and how I can save this plant?
The top part is dead and the most likely cause is overwatering. This plant is officially known as Beaucarnea recurvata and is a plant for high light and dry conditions. From the picture it looks like there is no drainage in the pot which might contribute to the death of the foliage.
There is still hope for this plant. Take some sharp pruning shears and cut off the dead foliage. Put the plant in a dry sunny spot and wait. If there is no new growth in six to eight weeks then the root rot has gone too far for it to recover. These plants will bud out from old growth. Do not water this plant until you see new growth and even then water only sparingly.