You need something on the monster that changes when it dies. That could be a flag called "dead" that gets set, or a hit points attribute that is below zero. I am guessing you have already set this up.
Then you need to have the objects notice when it is dead. There are two approaches here, and which you choose depends on what maintaining an object means - you may find it convenient to do some one way and some the other.
The first approach is to change the objects when the monster dies. This would work for locked exits and containers. This would be a script that runs when the monster dies:
msg("Hurray you killed it!")
bigchest.locked = false
exit_to_next_room.locked = false
The second approach is for the object to check if the monster is dead when the player tries to do something. Say there is a vase that can be smashed, on the SMASH verb, you might do something like this:
if (monster.hits < 0) {
msg("You smash the vase.")
vase.parent = game
}
else {
msg("You cannot smash the vase while the monster is protecting it.")
}
I hope this is enough to point you in the right direction (and you can cope with code to some extent).