Yes, there are many MCUs with internal oscillators that require no external clock sources.
Most MCUs have several clock sources, and a clock source has to be explicitly selected to be something else than a default. The default is one of the internal oscillators. There may be more than one, in fact.
In some MCUs, the clock configuration is permanent and comes from a special "config word" written into the MCU by the programmer device. This "config word" is known by many names, e.g. "fuse word", and it may reside in the code address space, or outside of it.
In other MCUs, the configuration is volatile and is programmed into the clock control registers by the firmware as it starts up. The bootloader may change the clock configuration, and then once the firmware runs it may make further changes as needed.
MCUs with complex clocking have "clock watchdogs" that use the internal oscillator to detect presence of an external clock signal. When the external clock fails for any reason, the MCU can automatically switch to the internal clock as a fallback. The firmware can respond to it in an interrupt handler, and can take necessary recovery/failsafe actions.