Sorry, I don't know. If you don't get a reply here, clip a leaf and take to nursery! Maybe the armadillos collect plant tags.

i would propagate some smaller pieces ... being very aggressive in cleaning them [a much easier job] .. and when those have rooted.. i would get rid of the old monster ... and to be clear ... when they say rinse it with water ... they mean a spray just short of ripping up the tissue ... not just a low pressure rinse .... i suspect they will root easily: https://duckduckgo.com/?q=Cordyline+fruticosa&t=ffcm&ia=videos&iax=videos might be interesting to compare how similar the propagation is ... getting a new plant rooted... is changing your very old plant.. into a vibrant new babe ... plus the new media.. etc ... by the time you are done.. you will probably have duplicates to spread all over the family ... or friends .... and.. while i was rooting some cuttings.. i would leave the old plant alone .. until i succeeded with rooting new ones ... btw: besides the webbing.. have you seen any other damage consistent with mites??? .. its called stippling .... https://duckduckgo.com/?q=spider+mite+damage&t=ffcm&iax=images&ia=images ken https://hgic.clemson.edu/factsheet/integrated-pest-management-i-p-m-for-spider-mites/

From what I can make out in the pictures I’d say Chickweed.

Leaf outline is generally like hybrid anthuriums that came on the general market awhile back. And if not one of those it will be some other arum family plant. Of which there are many.