Hi! They are called Cordylines and are lovely plants. are you able to post a picture here as I am not terribly sure about the top growth going droopy. The bottom leaves do die off to form a trunk and the top growth is naturally spikey, so drooping may not be good. They like damp free draining soil, esp in summer, so it also depends on where you live. They will get limpy top growth in very warm areas.

I added a picture of my plant above my name. I need to find out if this plant can be saved. It has been like this for a week. It used to be nice until i took off the bottom leaves and probably over watered it.

It might be root rot from over watering as that does affect top growth - the leaf colour looks OK, so adding drainage should save it.

Thanks

The grow well in the wetter parts of the UK (think NW US/Vancouver weather) as long as they have good drainage and rare hard freezes. They also pup at the base, so even if the worst happens to your Cordyline leave it and it should regrow from the roots.