They have a mechanism so the DAG is single ended, which means if 10,000 senders make a payment they will verify each other and there is only one at the end. This is a high volume transaction tech used on IoT, which means there is a huge amount of transactions per second. Your payment will usually get verified in milliseconds while on blockchain it takes 3-5 seconds. If a machine plugged into the network is appending his sensor data to the network there is a continuous stream of transactions so the scenario where there is a very long time world wide without a transaction if very much unexpected.
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I think you got something wrong here. There can be multiple DAG endings (called tips) in IOTA. The system is designed in a way so that participants are motivated to validate more recent transactions and especially those that have not been confirmed before (=tips), though, else the system would not work. You can view a live visualization of the IOTA tangle at https://tangle.blox.pm/.