A document mentioned that someone was unable to return to his home country to perform “last rights” for a dying or dead parent.
Rights are legal or moral; rites are religious or social (compare rituals). Overall, rights is far more common, but last rites is far more common than last rights (“This government is taking our last rights away from us!”). There is very rarely a last rite, and a last right is almost non-existent. (Compare last right, as is “This party will last right through the night!”.)
One type of rite is a rite of passage, which term was coined by Arnold van Gennep in 1909, but didn’t become popular until the 1960s. A right of passage is a term from maritime law, but may also refer to an easement on land (also referred to as a right-of-way).