fawnee0214, goats are not silly; their instinct is to 'raise their heads and browse'...and their reaction to temptation is to eat.
Oxalate is the poisonous element.
I do not know how much oxalate is in the leaf of Dracaena. Maybe no one knows.
If the goats ate a small quantity, it might not be problematic. Different story with cats.
Goats are ruminants; different from cats.
Free-range goats eat all types of vegetation - bitter, thorny etc. with no ill effects. Other goats? I plead ignorance.
Goats are indestructible.
If they salivate excessively, refuse to eat or stop chewing their cud; these might cause me to call in a vet.
I do not know what routine they have trained you into but at their next feeding, offer them their favorite diet and if they are unenthusiastic, call that vet.
I think that they will be OK.

Here's what Mr Subjunctive's commentary (one of the most comprehensive ones on houseplant toxicity I've seen online) has to say about dracaenas:

"Dracaena deremensis cvv. ('Janet Craig') ('Warneckei') I found shockingly little information on Dracaena spp. Neither Toxicity nor Handbook includes any Dracaenas, and the lists to be found on the internet disagree about whether or not they are toxic, though there seems to be some consensus that they are dangerous to cats and dogs but not people, reptiles or amphibians. (The reader is advised to be skeptical.) A few internet lists have Dracaena marginata down as toxic and the other Dracaena spp. as non-toxic, which makes me think that marginata might be a bigger risk, but it's really very difficult to tell. I'm fairly certain they can't be very toxic to humans, on the grounds that there are so many of them out there that if they were killing people, we'd be hearing a lot more about it. "

Here is a link that might be useful: Houseplant Toxicity

Thank you! I don't think they are toxic, at least not to goats in small quantities. By the way, I have draceana marginata.

The goat hasn't displayed any symptons of posioning and it has been about a week. I do know that goats are browsers and eat everything on sight by instinct. I just was mad at her for eating my plant. Though its my fault not hers! Thanks again!

Toxic is quite a relative term. In this context can be from a stomach ache to fatal. So you need to really be careful & read up first.

I believe there is some info. that Dracena CAN be harmful to people hence the name 'dumbcane'.

fawnee0214, a final point. You may do well to cut back the plants well below the chewed area. "When a goat chews on a plant, it (the plant) dies". I cannot vouch for this, but too many people have said it.

Dieffenbachia is known by dumbcane, not dracaena The level of calcium oxalate crystals is very high...so high that we should be careful when pruning or transplanting our dieffenbachia. The itching and stinging can be very significant. I learned the hard way.

Oops, thanks Rhizo,

Bit of a brain glitch, I guess. Sorry & thanks for catching it!

Hey, they both begin with a 'D' and end with an 'A'. That's reason enough for a glich, in my book, lol.

fawnee0214, I could not resist. D ahli a?

Didieria, Deuterichonia, Duvalia, Denmoza....