Cowerdly does not simply mean bad. Saying that sacraficing your life to achive a goal is cowardly is nonsense.
They suppressed there fears, that’s what bravery means. You can be brave doing horrible things. Mao was brave, Hitler was (at times) brave. You are falling into the halo issue, saying that if an act was bad it must be bad in all ways.
Natural languages are full of ambiguity, and yes that use sounds wrong cause your talking about a particular person.
And if you really wanted to say that it was Chris’s money, how about “Chris lost Chris’s money.” It sounds awkward to me cause my English only allows use of they in the singular if it is an abstract person, not a particular real person.
I mean its not like “Chris lost his money” is unambiguous, it is not at all clear to me weather the he refers to Chris, or someone else. That would probably be clear in discourse because of context.