Out of that group, donors are checked against databases of known giving history and net worth. These databases aren't always accurate or comprehensive, but it helps fundraisers to ID people who might be able to give more--sometimes a lot more.
When high-value prospects are IDed, they usually get assigned to a major gift officer who starts building a personal relationship to solicit very large gifts. This is where the charity makes the majority of its revenue. I usually see 95% of revenue come from the top 5% of donors, largely individuals.
If you're uninterested in receiving lots of mail, most charities will try to accommodate that request. However, resources are limited and dealing with the problems of $XX level donors often takes second place to the problems of $XXX,XXX level donors. I've seen stacks of returned direct mail several feet high from people who moved, died, wanted no more mailings, you name it. It was always on the to-do list to remove those names, but never at the top of the to-do list.