Looks like a Cordyline .
I don't grow them , but my neighbour did so my knowledge is based on his .
They were huge and used to shed all over my garden .
They aren't cheap - so worth a little resuscitation .
It might have started out as a house plant .
Originally from Australia - they don't enjoy our English winters so next winter cover it up with some old carpet , fleece or a chimney pot .
Doubt if the problem is slugs - those leaves aren't tasty .
But you need to protect it just in case they are enjoying the new shoots . There are more slugs and snails than ever in the UK .
I'd give it a prune , a slow release feed and gently loosen the compacted soil around it .
A coloured Cordyline will tolerate semi shade and the green ones like full sun .
If you find any bugs you might be able to wash them off with some water made frothy with Fairy Liquid , but from the photo it looks like the cold has affected it .