If a person got married and for some reason it didn't work out, and the papers have expired that immigration had, how soon can the person try again

The marriage is valid even if the immigration papers expire. The couple would have to get a divorce to end the marriage.

There is no specific rules about this issue BUT if you already submit an adjustment of status then withdrawn, you must have strong evidence to prove to immigration that this second marriage is bona fide... not because you want green card. Be prepared for fraud interview by immigration officers... this won't be easy. In many cases, there were more than one interview.

I recommend you seek help from experienced immigration attorney before you remarry and submit new application.