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As long as the stems are still pliable, it should come back. These articles should help: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm, https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

Browning tips on plant leaves is quite common and can be caused by a few issues.
Most are easily remedied.

Here are some articles for you.

http://mrec.ifas.ufl.edu/foliage/folnotes/cordylin.htm
https://www.gardeningknowhow.com/plant-problems/environmental/what-causes-brown-edges-on-leaves-of-plant.htm

This is a cultivator of the Ti plants or Cordylines.
The exact variety is unknown. They come in beautiful shades and colorings.
Here is a link with more information.

https://www.gardeningknowhow.com/houseplants/ti-plant/growing-hawaiian-ti-plant-indoors.htm

You could have a Cordyline. There are varieties with spiky leaves, including burgundy. Check whether the picture matches:
https://www.rhs.org.uk/advice/profile?PID=543

Or a Dracaena:
http://pss.uvm.edu/pss123/foldfm.html

Also check this site:
http://miami-dade.ifas.ufl.edu/fyn-publications/palms-cyadsA-E.shtml

That appears to be the start of a fungal infection. Wettable sulfur will kill of anything in the soil, and dolomitic lime will help to keep the pH stable while this is taking place.

Here is an article that will give you more information on the care of these: https://www.gardeningknowhow.com/houseplants/ti-plant/growing-hawaiian-ti-plant-indoors.htm

This is usually a sign of infection in the soil. This is typically caused by overwatering, inadequate drainage in container, or poorly aerated soil. Can you include a photo? If it is wilting at the main stem, then it is likely too far gone. If there seems to be some rigidity to it still, then you can try wettable sulfur. This will kill off anything that is able to be killed.