Yes, a wrong canonical tag can take a page out of Google’s results, but not the way a penalty would. The page isn’t being punished; it is being canonicalized away. When your canonical names a different URL, you are telling Google that this page is a duplicate and the other one is the version to keep, so Google folds the two together and indexes the target instead. The page you wanted can quietly fall out of the index, with no 404, no warning, and nothing broken on the page itself, because your own tag instructed Google to treat it as a copy.
That distinction matters because it changes where you look. A page that vanishes from a wrong canonical hasn’t tripped a quality filter or earned a manual action; it followed an instruction you gave it. So the people who shrug and say canonicals can’t really hurt you have it backwards, since a mispointed canonical is among the most common reasons a page silently disappears, and it is often a page that was working. The people who see a page gone and assume a penalty have it backwards too, because there is nothing to appeal and no penalty to recover from, only a tag to correct.
So when an important page drops out of search and the page itself looks fine, check its canonical before suspecting anything worse. Look at what URL the tag names, confirm whether it points at the page itself or off to another one, and if it is aimed at the wrong target, fixing that single line is usually what brings the page back.