If you look carefully at the tuber, you should see some tiny hair-like roots coming out of one end. That is the bottom. Sure, plant them in a pot and see whether they grow. I am just now potting some up, as they are just now starting to break dormancy. I agree, it is hard to tell the top and bottom of some. I also purchased some which fell apart. Actually when I started looking at them, I realized fairly quickly that there were several tubers wrapped around each other. I actually slowly twisted them apart, and got potentially more plants for the price of one. Now that is a good thing. Not all tubers will produce plants as some are there merely to store food. There needs to be an eye, and some eyes are very hard to see at first. I examined one just yesterday, and thought that there would probably be no plant coming from this particularly huge tuber (10" long). This morning, I can see the eye has swollen, and I know that I will have a beautiful red cactus style dahlia this summer which will grow to about 4 feet. Yahoo ! That is one I really wanted to save and multiply. Here is a small tuber, somewhat similar on both ends, but there are roots on one. These have developed over the past few weeks in a moist mixture. Originally, one could hardly tell the difference. That is why I lay it horizontally to help me determine where the roots are. Once planted the top end will definitely be up. Here is what a typical dahlia from the package looks like. Notice the stem. As you can see, there are many eyes on this one. Some folks like to cut off all but one eye. I like to get my exacto knife out and split them, making more plants. Read up about that first though. Here is a long tuber. One can hardly see the difference. If one looks VERY closely at the right hand side, one sees the eye starting to develop. Here is a closeup of the developing eye....starting to leaf. Isn't Mother Nature wonderful?

I would cut it down to within about an inch of the tuber, and let it re-grow.

Rabbits do this in our garden if we don't put chicken wire around the whole field. They do it in the rose garden, too-- & look you right in the eye while they bite off a stem & leave it there, then hop away! I tried blood meal in the rose garden & that worked until the first rain & then they were right back at it but the big garden is just too big to do that so the husband puts 3' high chicken wire around it until the plants get a couple of feet high. They don't seem to like the plants after they get big-- too tough I suppose.

Well, you'll get a lot of differing opinions about whether or not to cut the flower stem (inflo). During rooting, if leaves start to generate, but then stop, I'd cut it off. Or if you've got lots of other plumeria blooms to enjoy, remove it now. Morning sun might be OK, unless you're in the mid- to upper 90s or low 100s and have very low humidity. In that case I'd probably put it in dappled shade. How long (in inches) is the broken section? The larger the cutting, generally the easier it will be to root...at least anything over 14 inches will be easier than, say, 5-6 inches. Hopefully someone with more 'California' experience will chime in! We have a totally different climate here in Virginia in the summer. We're hazy, hot, and humid, and our night temps usually stay above 65 degrees thru June, July and August. Daytime highs around 80 - 95. So we can usually leave a cutting in full to part sun. The haze cuts down the rays a bit. And we also get rain, so we have to keep cuttings protected from too much moisture. But the humidity is so high that we rarely have to water the soil. They'll root in 'humid' soil just fine!