Examples of things that are undefined in terms of living and non-living
People expect viruses to be alive but they are defined as non-living.

This is actually one of the most widespread misconceptions I see. I think it's just one of those interesting but dubious factoids that spreads around in dinner party conversations. There certainly are some who take that position. But, after 11+ years of formal university education in biology, I can't think of a single professor or colleague who firmly embraced the position that viruses are non-living. Most (including myself) have been firmly in the camp that viruses are, in fact, alive. And the rest are more-or-less agnostic or ambivalent on the topic.
There's an intesting mini-debate between experts on the subject found here, I'll share this quote from one of the participants below because I think it's on point.

&quot;In many ways whether viruses are living or non-living entities is a moot philosophical point.&quot;

There isn't one single, universally accepted definition of life. So ultimately, the answer to whether viruses are living or not will depend on ones chosen definition, and that's the case with most other controversial things.
However, viruses are unquestionably classified as biological replicators. There's a review on that topic (found here). It also includes discussions of other replicators which some experts also think of as living entities (but many don't). Examples include certain genetic elements like plasmid and integrons.
One notable exception that I didn't see mentioned in that review is prions. The first virology professor I ever had strongly advocated definitions of life that were inclusive of prions, but I haven't found that position quite as common among other academics. I'm a bit more agnostic on the prion debate, because it's hard to find prion-inclusive definitions of life that arean't also inclusive of something like an inorganic crystal.
The problem is that scientists like consistent definitions that don't have lots of exceptions, or require us to split existing categories. Between viruses, plasmids, and prions, there's a lot to talk about in terms of what characteristics they share with other life forms and what they lack that makes some question their classification. It's also interesting to consider whether any of the attributes common to living things occur in silico (or if they could in the future).