Part 1:
Add a new dynastic rule, entitled: “Bleeding to death”, as follows:

Any Einherjar who has no Statistics with a value greater than +1 dies and becomes owned by no Valkyrie nor by Loki.

Upon the adoption of this proposal, the Allfather may determine that any one or more existing Einherjar shall be exempt from the “Bleeding to death” rule, and shall make appropriate amendments to the “special powers” of those Einherjar to state that they are exempt from this rule.

Part 2:
Amend the first sentence of the rule “Einherjar” so that it reads as follows:
There is a wiki page called Einherjar which contains a section named for each Valkyrie that has recruited an Einherjar, a single section named “Unrecruited Einherjar”, and a single section named “Dead Einherjar”.
Also add to rule “Einherjar” the following text:

The “Dead Einherjar” section shall list the names and statistics of dead Einherjar.  Dead Einherjar are not owned by any Valkyrie and may not be recruited by any Valkyrie for so long as they are dead.

(note that “fallen” (i.e., owned by Loki) and “dead” are two different things).