These modes are defined in the Hayes command set, which is the de facto standard for all modems.
The +++ escape sequence is rarely used, and may even be disabled to avoid malfunction in case these characters are legitimately a part of the data stream (ignoring the 1-second pauses).
Today, most modems are configured with the characters "&C1&D2" in the initialization string, or otherwise behave this way by default.
However, when modems are used for fax and voice (audio) communication, they rapidly switch between command and data modes several times during a call.
Other common out-of-band messages are notifications from the modem that data was lost because the computer is sending data either too slow or too fast, or that the modem hears an unexpected dial-tone on the line (meaning the caller probably hung up), or that the extension handset was picked up or hung up.
In this case stuffing means two DLE's characters in a row are interpreted as one literal byte with value 0x10.
Unlike in standard dial-up data mode, dropping DTR isn't an appropriate way to resume command mode since a hangup is not desired, and an escape code with mandatory pauses isn't suitable either.
DLE is never used in standard modem-to-modem data modes such as the one used for dial-up Internet access, at least not by the modem itself.