When attempting to respawn after all playable units (who have been added as respawn points using BIS_fnc_addRespawnPosition) have died, the game never leaves the "loading" screen. Additionally, you are able to move around and fire your weapon (you can hear this, and the other player can see it).
It appears that only the first player to die experiences this issue, with the second player being able to respawn normally at a static respawn position (not one of the dead players' bodies).
Running a custom multiplayer co-op mission which makes use of the ArmA 3 Respawn framework detailed [url=https://community.bistudio.com/wiki/Arma_3_Respawn]here[/url]. Respawn type set to 'BASE' and respawn positions added using a combination of the respawn module (as a static base respawn) and BIS_fnc_addRespawnPosition to add mobile respawn points on both playable units.