When we had the bathrooms remodeled, we wanted to install grab bars to help as we get older. In addition, we choose sturdy metal towel rods, not as a grab bar, but realizing they may end up being used as one in an accident.
And sure enough, Linda tried to use the towel rod to keep her from following, but instead of helping, it gave way. The towel rod is anchored at both ends, with a metal rod between them, but one of the ends gave way, allowing the metal rod to fall off.
The metal ends are attached to a post on the wall with a small set screw on the bottom.
Taking the ends off, we expose the two metal posts.
The posts are attached to the wall with two screws. Of course this is a marble tile wall, so there are holes drilled into it and an insert plugged into the hole; the screw goes into the insert.
The end which failed seems to be missing the insert, which means one of the two screws was not secured into the wall. (It's possible the insert was shoved back into the hole and dropped down behind the tile wall. In fact it appears that the tile wall is a false wall attached to 1x2 wood strips on top of the previous wall.)
So we have a couple of possibilities. We could replace the towel rod with a full-blown official grab bar, or we can re-install the existing towel rod. Using an official grab bar would seem better, but since the wall is a false wall, with just the tile and it's cement backing, we would need to use the same sort of insert as the towel rod used (or was supposed to use). So while it might be a slightly larger screw/bolt and insert, it would still be attached to the same wall, in the same way. (As opposed to attaching the bar by bolting it into a 2x4 or other solid structure inside/behind the wall.)
So we decided to just install an appropriate insert in the missing hole, and put the towel rod back up.
