As @Mariusz explained you got the error 'trying to dereference a null object' becuase you are using a <= operator with String. <= is a mathematical operator, and cannot compare strings. 

(For Contact c: cons) {
// it is read as : for every contact c in the cons list
// c is a variable that holds each contact record in that list
// cons is a list of contact records returned by the SOQL 
// we loop through each record in that list to see if the Email__c field has a value that ends with 'it.works.com'
}

c.Email__c.endsWithIgnoreCase('it.work.com'))
// instead of doing a wild card search in the SOQL, i used the function endsWithIgnoreCase becuase it specifically addresses your use case

massupdate
// In salesforce it's easy to hit governor limits. Hence you need to adhere to certain best practices. 
// instead of updating records one at a time, I am collecting all records that need to be updated in a list which i named as massupdate
// Update massupdate means update all the records at the same time. 

Try this code: 
 

// Create a list to collect all the values from the Join_Date__c picklist 
List<String> joinDates = new List<String>();

// this is how you collect all the picklist values
Schema.DescribeFieldResult fieldResult = Contact.Join_Date__c.getDescribe();
List<Schema.PicklistEntry> pEntires = fieldResult.getPicklistValues();
 
for (Schema.PicklistEntry pEntry : pEntires) {
    String pe = pEntry.getValue();
    if (pe.startsWith('1') || pe.equals('2000')) {
        // this is how you add all the picklist values in the list above
        joinDates.add(pe);
    }
}

// create a list of contacts to hold all the records that need to be updated
List<Contact> massupdate = new List<Contact>();

// Create a list of contacts whose Join date is in the list 'joinDates'
List<Contact> cons = [Select Id, Name, Email__c 
                           from Contact 
                           Where Join_Date__c IN :joinDates];
system.debug('Check the number of records in the list above' +cons.size());

// Loop through all the contacts in the above list returned by the SOQL query
// if in that list, there are any records whose email ends with 'it.work.com', 
//then replace that value with blank, 
  For(Contact c: cons){
    if(c.Email__c.endsWithIgnoreCase('it.work.com')){
        System.debug('>>>>>>>>>>>>>>>>> ' +c.Email__c);
        c.Email__c = null;
        // after making the Email__c field blank, add the record to the list 'massupdate'  
       massupdate.add(c);
    }
  }
// outside the for loop, check if the list is empty or not
// if the list is not empty, then update all the records in the list
if(!massupdate.isEmpty()){
 update massupdate;
}