The lowest radio receiver IF that I have found to date is 18 kHz, used in the various Racal SSB and ISB outboard adaptors (RA63, RA98, RA121, etc.) intended for use with the RA17 series of receivers.
These took their feed from the 100 kHz final IF of the associated RA17 family receiver. Another conversion was necessary in order to facilitate the inclusion of an on-board AFC loop for pilot carrier transmissions, thus obviating the need for arranging for AFC control of one of the receiver oscillators.
So why 18 kHz? Here’s an attempt at post facto rationalization: Racal used multi-section LC low-pass and high-pass filters for sideband separation, and I imagine that these were easier to implement and had steeper slopes (on a per kHz basis, not a per octave basis) at lower frequencies. So the goal may have been to have a final IF that was as low as reasonably possible. Given that the input bandpass was 94 to 106 kHz, that band, and in fact somewhat beyond it, would need to be free of any IF harmonics. So 18 kHz, with 5th and 6th harmonics at 90 and 108 kHz respectively, was about as low as was workable. The 118 kHz oscillator frequency was also clear of any IF harmonics.
Also, for greater sensitivity, the AFC discriminator worked on the 5th harmonic of the 18 kHz IF, namely 90 kHz, which was another reason for the harmonics to be well clear of 100 kHz and the passband.