I've always found Sag. subulata to be rather slow to adapt. Once it settles in though, it's a real weed.
That said, roots melting might kill the plant. Ultimately it's the crown that's most important to the plant's survival - both roots and leaves can regrow as long as the crown's alive - but large-scale root melt may be indicative of a plant on its way out. How long ago is "recently"? How much of the root system is dying off? A little bit of browning at the ends is probably fine.
I wouldn't chop off the leaves. Trimming a few dying leaves off of a healthy plant is once thing, but hacking off the entirety of one that's already struggling can kill it. Wait until the plants have acclimated to start giving haircuts.