I am looking to purchase a coop that was subleased to me 3 years ago by a broker. The owner had an agreement with the broker (that says it expired 90 days after signing) that states if renter decides to buy the apartment a fee of 6% would need to be paid. Is anyone familiar with these agreements, and are they still valid 3 years later?

if it says it expires, it expired. they can't inforce anything 3 yrs later.

Is it possible that the agreement could expire and still have a valid clause that states that if the renter purchases the commission should be paid?

First, from what I can tell 3 yrs. later the 90 days is up obviously, so that's expired.
Second, the 6% would usually be paid by the owner, not renter.
I have put such into rental agreements and if there is a time-frame that trumps all.
Three years later I wouldn't worry about it if I were you.