What kind of emission would your FM transmitter produce if its microphone failed to work?

When you key a transmitter, the first thing it does is generate a steady Radio Frequency (RF) carrier. In an FM system, the audio from the microphone varies (modulates) the frequency of this carrier. If the microphone fails, no audio signal reaches the modulator circuit. Without an audio input to shift the frequency, the transmitter will simply output that steady, continuous RF signal exactly at the center frequency. This is referred to as an "unmodulated carrier" or commonly a "dead carrier." It would not suddenly become amplitude or phase modulated, because the modulation circuits are starved of any input. It also does not mean the transmitter stops transmitting entirely; the RF power is still being radiated.