Es decir, que quedas "rezagado" hasta el siguiente encuentro ¿no?
No queda rezagado.
Citar
If an investigator is ever reduced to 0 Stamina while in Arkham, the investigator is knocked unconscious. He must immediately choose and discard half of his items and half of his Clue tokens (rounded down), along with all retainers (if any). The player then immediately moves his investigator to St. Mary’s Hospital. The investigator is restored to 1 Stamina and has no further encounters this turn. The investigator may take his next turn as normal.
Es decir, simplemente se desplaza hacia el hospital (o hacia el sanatorio si corresponde al caso), recibe 1 punto de resistencia (o de cordura si corresponde al caso) y allí finaliza su fase de encuentros (o simplemente no la tiene, si aún no ha tenido lugar). Rezagado sería si en el siguiente turno no pudiera moverse, y no es el caso.