i think it depends on the individual.. and yeah obviously on what terms the break up happened on.. sometimes the reason for breaking up is to get some space from ur partner.. or watever..
but if ur just going out.. and things arent worknig out.. then well u can try being friends.. and yes sometimes feelings do get in the way.. but if ur both being mature bout it.. i think it works out well..
sometimes the opposite happens.. ur best friends with someone.. then u start going out.. but when ur in a relationship like that.. things go very wrong.. and u breka up.. and then the friendship is lsot as well.. ive seen that happen.. and it aint pretty.. cus u get left with nothing..
honestly.. if ur good at having control of ur feelings.. there is no such thing as an impossible solution then :)