There are many creatures that have death triggers, and when playing Fake Your Own Death on those creatures, only their base effect triggers, but they do not return to the battlefield. It looks like the treasure does still get created.

I've also experienced issues with "Fake your own death", even though for me the card usually works fine, there are some issues with automatic sacrifice during the end step:
Yesterday I played "Jaxis, the Troublemaker" to create a token of an other creature (a "Forge Boss" I think), to then cast "Fake your own Death" on that token. This creates a token that should be sacrificed at the beginning of the next endstep, thus triggering the dying condition on "Fake your own death", which did create a treasure token, but did not enact the second part in returning it to the battlefield under my control (which would have given me an additional treasure token and card at the beginning of the next endstep (or this endstep if "beginning of end step" is a phase and not just a point in time that's over after the initial sacrifice), or whenever else the returned token dies). This feels very wrong, since the "Fake your own Death" triggered, so sacrificing is a valid way of dying, but then arbitrarily the rest of the card text was ignored. Am I missreading the card, are there rules about some card interactions not written on the cards or is this an implementation mistake of arena?