Some candidates have the personal or family resources to self-fund their graduate studies, or already know that they are willing to take on debt for them (disregard whether this is a good idea, which has been addressed before). They still, however, need to actually be admitted to a graduate school, and having funding doesn't guarantee admission.
The ability to self-fund obviously makes it possible to take unfunded offers, but are there any other ways to actively leverage this funding situation during the application process? Should the applicant inform schools that they would take an unfunded offer, and, if so, when should they (e.g. when applying, after being put on a waitlist)? Are there specific strategies that a candidate might be able to use when choosing schools to apply to?
I suspect that answers to this question might be field-specific, so I won't necessarily specify a field. Answers discussing the differences between fields might also be interesting.
Note that I am not in this situation, so I won't really be able to answer those kinds of clarifying questions. I just thought it was an interesting question that was inspired by but not directly addressed in this question.