Will MEPS give off toxic gases in my home?

No. MEPS begin as tiny styrene beads that are impregnated with liquid pentane- a colorless hydrocarbon which does not cause any health problems except at high levels of concentration.
When heat and steam are applied to the beads, the pentane causes them to expand to more than 30 times their original size (when the plastic is in its bead form, pentane accounts for about 6 percent of the material by weight). During the expansion process, this drops to about 3 percent, and within 6 weeks to 2 months after cutting pentane content declines to less than one-quarter of one percent. By the time of occupancy, the pentane content is negligible. MEPS contain no formaldehyde.