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Can these surfaces "get cancer"? As in, for some reason, the reaction continues way beyond simply healing the crack?

Cancer is unregulated growth. Since the authors are moving towards non-biologically derived catalysts, there will be no life-derived chloroplasts like they are currently using. So, you're asking can a non-biologically derived material spread indefinitely beyond the filling in of small cracks in its surface? I don't think there's a risk of that based on the article. Is there another non-biological material that spreads in the manner you've described?

I think cancer is a more specific concept than just "unregulated growth." Cancer is a phenomenon that occurs when a valid "self-replicate then die" program has a similar encoding to a "self-replicate indefinitely" program, such that random-noise damage to the program's stored representation can result in the former being rewritten into the latter.

Whether or not the substrate is biological, I would think that you'd still have to worry about ensuring your program is encoded in such a way that the part of it that turns it off can't be damaged without disabling the program as a whole.

Hope not - otherwise an alien civilization might find us someday with everyone frozen in carbonite like Han Solo.

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