Renal does not participate in the NRMP medical specialties match, so it wouldn't do any good for your brother to register with NRMP. As far as I know, there's no centralized list of unfilled programs for this specialty. You will have to make calls to individual programs and otherwise just ask around. Renal programs take their fellows basically in a rolling admissions process -- they don't have a match.
I think your best best would be to apply for programs in the next application cycle. Often last-minute positions open up at programs during the process, and they will offer these to candidates currently applying to their programs who would be available to start the next academic year. I know several people who got spots this way -- they were planning on taking a year off after residency, but earlier positions opened up for them.
