Cassettes and chains do not wear at the same rate (rate measured in: per number of miles done). After fitting a new cassette and a new chain (assuming of similar decent quality), you can expect good performance (ie no slipping) for 3000km+ (YMMV) until the chain gets to/closely approaches the 0.75% elongation point. At that point the cassette/chain will continue to operate (and this is what
@Racing roadkill must be doing) but the cassette will quickly wear, and sooner or later (say another 1000km, maybe more, probably less) the slipping will start. If you just put a new chain on, it will slip (as
@Racing roadkill has discerned, so he replaces the cassette at the same time - entirely reasonable, based on the experience he has (and possesses loadsamoney to buy a new cassette twice as often (mileage-wise) as Mr Sensible (see below)). I suggest that
@Supersuperleeds is adopting the same regime and inevitably has the same experience.
But if Mr Sensible replaces the chain when it gets to/closely approaches the 0.75% elongation point (which is the widespread recognised best practice), then the part used cassette and the new chain will be fine (no bedding in required - what do you think is bedding in), and you should get another 'normal' distance life out of that chain too.
Mr Lucky (or maybe one who diligently changes at the 0.7% point) will get a third chain's worth of use out of the cassette.
Then change both, and start the cycle again. Happy non-slip riding. Here's one rider's experience.
I'm about to change my chain for a second time, on this year's second cassette, but it is not yet at 0.7%. On this cassette (Mar-end May) the first chain did 3200km (NB varied spring weather). The chain I'm about to change has done nearly 5000km (Jun-Oct - NB summer, not much in wet and majority decent rural (including A and B) roads).
HTH