Permutation City by Greg Egan

In Egan’s version of the future, society has developed technology which allows one to create a precise one-for-one digital Copy of themselves. This Copy is identical in every way to the original person, and is often used by the rich and wealthy as a way to obtain partial immortality following death. Those of the upper middle class may be able to afford a scan on their deathbed… but may not be able to afford to actually be simulated due to the price of computing power and server time, or may have to “live” with extremely slow processing speeds.