There is no deal, until the condition is fulfilled, satisfied or waived. Usually, the condition will relate to a specific matter like mortgage financing or the physical state of the premises. Once it is satisfied, then in order to confirm the transaction and make sure that there is a binding agreement between the parties, this matter needs to be documented within the relevant time period.
This documentation can be accomplished in several ways which include either both parties signing or just one party signing. If a waiver provision has been included since the condition might be to the benefit of one party only, then a Waiver can be executed by that party alone. In many cases, realtors will often have both parties execute an Amendment deleting this clause. This is unnecessary.