They can just unslot the augment and move it between gear sets.
It's always cheaper to buy another deathblock than to reslot it.
Jewelllers kit to do so would cost circa 50% more than just buying a new Deathblock for each item you wanted to slot it in...
95.0 DP per Deathblock
99.5 DP per Kit (995 per 10)
It's not a 50% difference unless you waste DP buying kits 1x1. They're almost the same cost. But, it's still ALWAYS cheaper to buy a new DB than reslot.
BTW, gear v aug is the same. Deathward will also protect from negative dot tick damage. Lifesealed adds %absorb for negative. Spells as source can be dispelled when you need it the most; eg. beholders. So, I count deathward as useless.
IMHO, DB is mandatory everywhere, but it's mostly just a matter of taste outside hardcore. You can do an entire life without it and then die over and over next life. If you're OK with random low-chance instant death now and then, there's no point.