Using the one trigger per object best practice, my trigger is not updating the results back to old values when an update (that would NOT be counted in the SOQL query) or delete occurs. Please see code below:

Class:

public with sharing class CompletedEvents {
    protected final Event[] eventOldList;
    protected final Event[] eventNewList;
    Set<Id> contIds = new Set<Id>();

    public CompletedEvents(Event[] eventOldList, Event[] eventNewList) {
        this.eventOldList = eventOldList;
        this.eventNewList = eventNewList;
    }

    public CompletedEvents(List<Event> events){
        this.eventNewList = events;
    }
   
 public void executeTotalConferenceCalls(){
        for(Event e : eventNewList){
            if(e.WhoId != null){
                contIds.add(e.WhoId);
            }
        }

        AggregateResult [] ars = [Select WhoId eventId, count(id) ConfCount
                                  From Event
                                  Where WhoId in :contIds
                                  AND EndDateTime < :date.today()
                                  AND isDeleted = False
                                  AND Subject = 'Conference Call'
                                  GROUP BY WhoId All Rows];

        List<Contact> updCon = new List<Contact>();
        for(AggregateResult ar : ars){
            Contact c = new Contact();
            c.Id = (Id)ar.get('eventId');
            c.Total_Conference_Calls__c = Integer.ValueOf(ar.get('ConfCount'));
            updCon.Add(c);
        }

        if(updCon.size()>0){
            update updCon;
        }
    }

    public void executeLastCompletedEvent(){
        for(Event e : eventNewList){
            if(e.WhoId != null){
                contIds.add(e.WhoId);
            }
        }

        Event[] eventList = [Select WhoId, Subject, EndDateTime, ActivityDateTime, ActivityDate
                             From Event
                             Where WhoId in :contIds
                             AND EndDateTime < :date.today()
                             AND isDeleted = False
                             AND Subject != 'B/D-Conference'
                             AND Subject != 'Cancel/No Show'
                             AND Subject != 'DD Meeting'
                             AND Subject != 'NRS-Conference'
                             AND Subject != 'Other'
                             AND Subject != 'Drop-In'
                             AND Subject != 'Business Review'
                             AND Subject != 'One-On-One'
                             AND Subject != 'Travel'
                             AND Subject != 'Professional Association Event'
                             ORDER BY EndDateTime ASC All Rows];

        Map<Id, Contact> cMap = new Map<Id, Contact>();
        for(Event e : eventList){
            Contact c = new Contact(Id = e.WhoId);
            if(c.Id != null){
                c.Last_Completed_Event__c = e.EndDateTime;
                cMap.put(c.Id, c);
            }
        }

        update cMap.values();
    }
}

Trigger

trigger MasterEventTrigger on Event (
    before insert, after insert,
    before update, after update,
    before delete, after delete){
    Event[] eventOldList = trigger.IsDelete ? null : trigger.old;
    Event[] eventNewList = trigger.IsDelete ? trigger.old : trigger.new;
        
    if (Trigger.isBefore) {
        if (Trigger.isInsert) {
                new CompletedEvents(eventOldList, eventNewList).executeTotalConferenceCalls();
                new CompletedEvents(eventOldList, eventNewList).executeLastCompletedEvent();
        }

        if (Trigger.isUpdate) {
                new CompletedEvents(eventOldList, eventNewList).executeTotalConferenceCalls();
                new CompletedEvents(eventOldList, eventNewList).executeLastCompletedEvent();
        }

        if (Trigger.isDelete) {
                new CompletedEvents(eventOldList, eventNewList).executeTotalConferenceCalls();
                new CompletedEvents(eventOldList, eventNewList).executeLastCompletedEvent();
        }
    }
    
    if (Trigger.IsAfter) {
        if (Trigger.isInsert) {
        }
        if (Trigger.isUpdate) {
        }
        if (Trigger.isDelete) {
        }
    }
}