Assume that you replaced failed DHCP server with a new one configured with the same scope. This can possibly lead to situation when your new DHCP server can lease addresses which were earlier issued by failed server if it was configured with the same scope.
To mitigate this you can use Conflict detection attempts setting which can be found on Advanced tab of your scope properties:
By default it is set to 0 which means that your DHCP server won’t attempt to perform any conflict detection before issuing an address. As soon as you set this parameter to something higher that 0, let’s say N, your DHCP server query the network N times before it assigns an IP address to make sure that address is not already in use.
Of course this is a good option to be aware of, but real solution here is to add extra DHCP server and configure DHCP Failover which is available in Windows Server 2012 or newer versions and ensures that you won’t need to have any headache if one of your DHCP servers fails.