The min. DR is currently not used by the implemented algorithm but is specified as a device-profile field by the LoRaWAN Backend Interface specification.
LoRa Server never decreases the DR as this could result into a domino effect. E.g. when your network is dense, then lowering the data-rate on one device will impact other devices so other devices might also need to change to a lower data-rate (following the ADR algorithm), and so on…
Note that devices have an automatic data-rate decay implemented so in case of disconnection from the network, they will lower their data-rate until they are connected again.