I think issues can be solved with communication and talked to both of them, but in the end, one tenant decided they had enough and forfeited their deposit to break the lease and move.

Try creating a single journal entry for Deposit As Rent (aka forfeit deposit on move-out).I was taught to use one transaction and post to multiple T-accounts for tracking purposes. 

At that point, they forfeited their right to life and they got EXACTLY what they deserved.

If you don't eventually close on a property, you forfeit that money.I'm just curious if anyone else has worked with a realtor/broker under this arrangement and what their thoughts/experiences were? 

According to the terms of our lease, they forfeited the last month’s rent and deposit when they breached the lease.

Both are forfeited if the option is not exercised within the term of the option given.So yes, you collect rent. 

In the state of IL would a landlord be considered violating any tenant's rights by requesting established tenant(s) to undergo a new rental application process as if they're a prospective new tenant that will now determine if their lease will  or will not be renewed  with the possibility of forfeiting their security deposit?

Some counties require the winning bidder to immediately pay the full amount due even before leaving the room, whereas other counties allow some period of time after the sale/auction to pay the balance due or the deposit is forfeited.  

In the event the application is approved and applicant fails to enter into a lease, the applicant shall forfeit this deposit.

What about just having each tennant sign a waiver that they stay at their own risk and they forfeit their right to sue ... and getting umbrella insurance?