Dreaming of cockroaches may signify a fear of letting others down if the dreamer is overrun by roaches. Fear of the roach inside the dream may signify health issues.
Being overrun by roaches symbolizes the dreamer's fear that his own strength is not enough to keep promises that are made to other people. This may be tied to feeling overrun by overreaching and over committing in his waking life.
Fearing the roach, which is a symbol of sickness, may signify the dreamer's fear for his own personal health. This can serve as a reminder to the dreamer to make sure his physical and mental needs are met.