Most modems use the Hayes AT command set. The modem's attention is gained by sending +++ surrounded by some idle time. Commands are then sent prefixed by AT.
Unfortunately, if the modem sees +++ during a call it may revert to command mode. The modem can then be configured by the caller. For example, the modem could be set to permit incoming calls only from the number "0", this would deny the system administrators access to the modem.
The attention command can be removed using AT S2=255. Of course once that is done no more AT commands can be given to the modem, so any other configuration of the modem needs to be done prior to that command.
Unfortunately, when power to the modem is applied the modem starts in command mode. So a carefully chosen console message could disable the modem.
The best solution is to select a modem that has a "dumb" or "select profile" DIP switch or jumper. These switches disable command mode and load the modem's saved configuration when they start.