Do the throes of death and the pains resulting from them or from illness alleviate sins?

Yes, everything that afflicts a person, whether it be illness, hardship, worry, sorrow, or even a thorn prick, serves as an expiation for their sins. If they endure patiently and seek reward from Allah, then in addition to the expiation, they also receive the reward for their patience. There is no difference whether what afflicts a person occurs at the time of death or before it. Calamities are expiations for sins for the believer, as Allah the Almighty says: (And whatever strikes you of disaster - it is for what your hands have earned; but He pardons much.) [Ash-Shura/30], and as the Prophet, peace and blessings be upon him, said: "No worry, no sorrow, and no harm afflicts a believer, not even a thorn that pricks him, but Allah expiates some of his sins by it."