What
@MissMac described is the safest approach for these tree's when cutting from the ground, like mentioned earlier the inner heart wood separates itself from the outer layer once the tree dies and the water / nutrients stop flowing. Also you want to be looking up, like any dead tree the tops are the first to go and ash has that characteristic of limb wood near the crotches getting extremely weak first.
Best advice I can give, cut these tree's down when there still alive, they dont die overnight, it takes a couple of years and thanks to nature itself, there are clues to a sick ash tree. 1st - some tree's under stress will seed out, and a lot of seed to. 2nd - canopy coverage will get thinner with time and the tree will loose all its leaves if any drought stress occurs due to already combating the borer. 3rd - wood peckers will attach the trunk and leave "blonde" spots that are very noticeable, its just bark peeled off so they can eat the borer. You start noticing these clues, its time for it to go before you have to play chainsaw roulette.
For those with tree's like these growing near homes, or area's with frequent people near by and need a tree service to work them up, its way cheaper for a service to take a live one down then a dead one, especially if its a climber, about 99% of all tree services that offer climbing to remove tree's will not touch a dead ash tree, they are to unstable to climb and either a back yard machine or crane is needed to take them down (big $$$).