I made pickled beetroots (with garlic, bay leaf, pepper, a sprig of dill and salt water), and after a month or so, the liquid in the jar is thick like a jelly, especially at the bottom... why is that? I think it happened with my other beetroot pickles too, but they were eaten after a few days so the jelly didn't have time to get thick. It doesn't smell bad.
No, it doesn't form a layer, just gets thicker at the bottom of the jar. Looks like egg white (but pink, because of beetroots...). I haven't seen it in store bought pickled beets.
It's dextran. It sometimes forms with particularly suggary lactofermentation -- carrots, beets, ginger-bugs, mostly. If you leave it alone and let it continue to ferment, it is very likely, but not certain, that the dextran will be metabolized away in the next two weeks. If that doesn't happen, it isn't bad for you, it's just a gross texture. So if you can get over it, you can still eat your beets.