Nick, when you enable the clock loss monitor/interrupt and it then triggers....the K60 will be automatically be clocked by one of the internal reference clocks....either the slow (32Khz IRC) or the fast (2Mhz IRC), depending on how the MCG registers are set up. See page 550 in the K60 reference manual for detail on FLL bypassed internal (FBI) mode.
So in your use case.....when the external Real Time Counter (RTC) clock source is lost.......and you have enabled the clock monitor+clock loss interrupt.....it will use the Internal Reference Clock sources (IRC).
A caveat.....if you use STOP, VLPR or VLPW modes, you must disable the Clock Monitor Enable prior to entering any of those modes, otherwise it will trigger a reset request.
About the clearest description I found is section 24.4.4, but there are so many cross references to other registers/bits that you need to jump around alot to those register descriptions in the reference manual to put all the pieces together.
It would be great to have PDF reference manuals organized like WikiPedia, with embedded links to other sections as noted. Someday.......