What can we do if a bride provides the cake topper, which she's gotten on the internet, LOVES, and gets to you at the last minute....and it turns out the topper is too heavy, or it's center of balance is poor, or it's topheavy....and you're just sure it's going to fall off the cake????

Brides I think believe that if the item's description includes the word "cake", it must mean it's just fine for a wedding cake.

Is there some sort of support or anchoring mechanism for such a problem??

If the cake is covered with fondant, your could try using royal icing to stick the darn thing on. RI dries rock hard and would hoepfully hold it on the cake.

This has happened to me twice too. My cake was fondant covered and I put 3 dowels into the cake a few millimetres above the level of the icing and placed a cake card on top and then put the topper onto that. I surrounded the topper with little flowers so that you couldn't see any gaps. I always ask now if the bride wants to provide a topper as not everything they want to use is cake friendly as you say.

I also placed the topper onto the cake at the venue at the last minute to avoid it falling off!

If the bride is to provide the topper, she has to get it to me ahead of time, well-packaged, so that I can do a custom support system. (pillars hot-glued to a custom cut cakeboard.)
Some toppers even have holes through which dowels can be placed to add security, in addition to the weight supports.

I almost had my first cake disaster because of that exact thing! Bride just brought the topper to the site (when I asked her about it before she said it wasn't heavy or anything). When I put it up it was very poorly centered, weight-wise, so it fell off while I was putting on flowers. Amazingly it only barely dented one of the cakes below it when it fell!! I ended up desperately improvising with a plastic lid of all things, but cleverly managed to hide it . I've learned to get the topper ahead of time, no matter what, and the best thing is like aine2 said, put a cake circle under it with the same doweling as if it were a cake, glue that thing down, and put it on at the last minute.