This was initially documented a long long while back, and is absolutely still the case - Death Mark activation hitting barrier Barrier will take all armor and let the troop survive (with no barrier, but deathmark still on). Just confirmed it using Celestasia. Also confirmed you don’t have to have any armor for barrier to block a deathmark (which I was unsure about doing my tests years ago).
Earliest mention I can see of it working this way was May 2017, though it likely always worked like this.
Also brought it up here:
I’m bringing this up because this interaction has existed for so long that the least disruptive “bugfix” to this weird interaction would be that Death Mark activation is completely blocked by Barrier, since a troop with barrier would historically always survive a death mark activation. Changing Death Mark activation to go through barrier completely would qualify as a balance change by removing long standing counterplay to Death Mark. Death Mark is a lot more reasonable than when we actually needed this as counterplay, though (the first linked post was from before Death Mark had a one turn grace period, bless and undying didn’t exist, and very few things were death mark immune). Either way, please consider the larger implications a given fix would bring.