Intermediate Frequency in FM receiver
The incoming radio signal isn't mixed down to exactly 10.7 MHz, that would be pointless. Rather, the incoming signal (which varies in frequency) is mixed with a stable local oscillator; the result is a signal that has the same frequency variations but centered around 10.7 MHz. 

This intermediate frequency is filtered through either tuned LC circuits or a ceramic resonator, but these circuits are not so narrow-banded that the frequency deviation is lost. The frequency swing of commercial FM stations is +- 75 kHz anyway, or 0.075 MHz, less than 1% of the IF frequency.