In article ,
(Snowbird) writes:

what's the shortest runway you've encountered with an ILS?

About the shortest I can think of offhand is the ILS 24 at
RID (Richmond, Indiana), 5500 ft.

KLPR in Ohio (just 8 miles from me at I64) has an ILS to 07
and is 5002 X 100. Uncontrolled field.

Chuck