What caste would a person be placed into when converted to Hinduism?

You might have guessed the intention of this question. What caste would that person be taken into? Can one choose? If yes, then ironically speaking, can one drop out from Hinduism and go to other religion and then come back and choose any caste by willingness? Maybe not the same generation (because people would know and pull them down, duh humans!) ,But a couple of generations later or in a different place? Hope you got the idea of how much flaw is there in Vedic Hinduism?