How does a stateless person (one who voluntarily renounced their citizenship while in country) provide identification, arrange travel visas, and get back into the US?
It does not appear there are any provisions for stateless people to enter the US or identify themselves therein. The US didn't ratify the UN Convention relating to the Status of Stateless Persons. If you manage to get into the US you will not be able to open a bank account or do anything else that requires ID.
It is legally impossible to renounce your USA citizenship whilst inside the USA. Renouncing it in a foreign country costs you $2300 in filing fees (plus, I would imagine, all your back taxes) :)
At that point, you become the problem of the foreign country. You aren't anyone to the USA, and you have to apply for a visa just like anyone else, because the USA does not have a visa waiver program with your country of citizenship. since you don't have one.
the pivotal factor in evaluating your visa application is whether you'll leave the US consistent with your visa, i.e. return to your country of citizenship. Since you don't have one, no country need take you, and the US might be stuck with you. So they won't issue you a US visa.
Also the small detail of having no passport to stamp it in!
If you found yourself in the kind of piccadillo that would qualify a foreigner for refugee or asylum status, the US would consider it just the same as others, since those statuses include right of residency. Some countries manufacturer stateless people, e.g. Syria will not grant citizenship to a non-Muslim born there.