How to have a generally usable class call an abstract method

I have several GameObjects which have the script HealthManager

     public class HealthManager : MonoBehaviour
         {
                 public int health;
                 public int maxHealth;
         
                 public DeathHandler deathHandler;
         
                 void Update()
                 {
                         if(health <= 0)
                         {
                                 deathHandler.Die();
                         }
                 }
         }
 

I have DeathHandler as its own thing because different GameObjects do different things when they die. Originally, I tried to do this using a DeathHandler interface, but it won't let interfaces be MonoBehavior so I can't use the serializability to pass in a script that implements DeathHandler.

I thought that the alternative would be to make DeathHandler an abstract class because then you can at least pass stuff in, but for some reason it won't let me make a subclass that also implements MonoBehavior

 public class SoldierDeathHandler : DeathHandler, MonoBehavior // <- This is an error
     {
         public void Die()
         {
             //code
         }
     }

How am I supposed to do this? I don't want to write spaghetti code that checks for every single GameObject type that can hold a HealthManager