Skipping segments does not work, when you are flying on cheaper fares. However, when flying in full fare F/J it does work. Example:

pax wants to fly FRA-SIN-FRA leaving 27th June coming back 30th July

He books:

TIP-FRA 23rd June
FRA-SIN 23rd June
SIN-FRA 30th July
FRA-TIP 2nd August

He then does not show up on the 23rd June in TIP... his itineray is cancelled. However... he then turns up at the airport in FRA on 27th June, and says, here is my FULL FARE ticket (with the TIP-FRA segment ripped out, obviously) and I would like a seat on this flight... since it is full fare, they will let you on the FRA-SIN segment, no worries, subject to availability.

I am not recommending that you do this, I am just saying it is possible

Cheers