By default, Quick Connect or the Active Roles Synchronization Service will replicate the exact state of configured attributes between two connected systems. So, if the source object has no value for a configured attribute, the target object will be cleared as well.
This may not always be the desired behaviour.
In order to modify this behaviour, it is necessary to leverage a PowerShell script.
For example, with two Active Directory connected systems, it may be desired to copy over a Display Name if it is set, but retain it if it has been set in the destination and has not been set in the source. The following script could be used in a Forward Sync Rule as a PowerShell step:
if($srcObj["displayName"]) # Check to see if the source object has a value in the displayName attribute
$dstObj["displayName"] # Returning the value of the destination object's attribute will cause no update to be performed