From the "Aviation Theory Centre Training Manual - IR LAW". The New Zealand version
"The purpose of the information on the 25nm minimum sector altitude diagram is to provide the pilot with a quick minimum safe altitude within a sector when an emergency situation in IMC has developed. A lower altitude may be flown within the area when the aircraft is following a promulgated route, a published flight procedure with a lower MSA, or VORSEC information."
NB. All NZ procedures (except two i believe) are based on PANS OPS II.
Not sure about the rest of the world.