The reason an unlosing agent might be interesting is that it doesn't have to have its values specified as a collection of explicit utility functions. It could instead have some differently specified system that converges to explicit utility functions as it gets more morally relevant data. Then an unlosing procedure would keep it unexploitable during this process.
In practice, I think requiring a value-loading agent to be unlosing might be too much of a requirement, as it might lock in some early decisions. I see a "mainly unlosing" agent as being more interesting - say an imperfect value loading agent with some unlosing characteristics - as being potentially safer.
Some have expressed skepticism that "unlosing agents" can actually exist. So to provide an existence proof, here is a model of an unlosing agent. It's not a model you'd want to use constructively to build one, but it's sufficient for the existence result.
Let D be the set of all decisions the agent has made in the past, let U be the set of all utility functions that are compatible with those decisions, and let P be a "better than" relationship on the set of outcomes (possibly intransitive, dependent, incomplete, etc...).
By "utility functions that are compatible those decisions" I mean that an expected utility maximising agent with any u in U would reach the same decisions D as the agent actually did. Notice that U starts off infinitely large when D is empty; when the agent faces a new decision d, here is a decision criteria that leaves U non-empty:
That's the theory. In practice, we would want to restrict the utilities initially allowed into U to avoid really stupid utilities ("I like losing money to people called Rob at 15:46.34 every alternate Wednesday if the stock market is up; otherwise I don't.") When constructing the initial P and U, it could be a good start to be just looking at categories that humans natuarally express preferences between. But those are implementation details. And again, using this kind of explicit design violates the spirit of unlosing agents (unless the set U is defined in ways that are different from simply listing all u in U).
The proof that this agent is unlosing is that a) U will never be empty, and b) for any u in U, the agent will have behaved indistinguishably from a u-maximiser.