The author continues his previous work, studying a relativistic fluid which consists of two phases, a soft phase in which the speed of sound is zero, and a hard one in which that speed is equal to the speed of light. The density characterizing the soft phase is less than the nuclear saturation density. The problem investigated consists first in extending the solution into the causal future of boundary null points at which the smooth spacelike segments comprising the achronal boundary separating the phases become null. He then studies the vacuum free boundary as a special case, the problem of continuation of a free-phase boundary, and finally the problem of its termination. The different cases of separation of soft and hard phases studied in the last part of the paper are particularly interesting. The whole study is very detailed and thorough.