Basically you can just use the condition script of the attribute customization combined with the Required Attributes For Condition precondition. Since you mentioned "previous values", which I understand are the "saved values", you will need some tweaks for it to work - you need to ensure the script only evaluates the "saved values".

Here is the sample code that I quickly write. Of course you need to do your own testing to accept it.

dojo.provide("com.example.RequiredByOthers");
dojo.require("com.ibm.team.workitem.api.common.WorkItemAttributes");
// Define non-local variables
var com_example_RequiredByOthers_WIs;
var com_example_RequiredByOthers;

(function() {
    var WorkItemAttributes = com.ibm.team.workitem.api.common.WorkItemAttributes;
   
    dojo.declare("com.example.RequiredByOthers", null, {

        matches: function(workItem, configuration) {
           
            // Create the key pair collection if not exists yet
            if ((typeof com_example_RequiredByOthers_WIs) == "undefined") {
           
                com_example_RequiredByOthers_WIs = new Object();
               
            }
           
            var id = "" + workItem.getValue(WorkItemAttributes.ID); // Force a string instead of int
            var modified = workItem.getValue(WorkItemAttributes.MODIFIED);

            if ((com_example_RequiredByOthers_WIs[id] == modified) && ((typeof com_example_RequiredByOthers) != "undefined")) {
               
                // the existing data has been evaluated before, return the existing value
                return com_example_RequiredByOthers;
               
            } else {
               
                // Not required by default
                com_example_RequiredByOthers = false;
                // Save the current state of the WI
                com_example_RequiredByOthers_WIs[id] = modified;
           
                // Do necessary checking against existing values and assign true or false accordingly.
                //
               
                return com_example_RequiredByOthers;
            }
        }

    });
})();

P.S. The script will be executed when the work item is loaded, and every time an attribute is changed. The two non-local variables provide a way to execute the script only when the work item is loaded, or when the work item is saved.