Negligibly for EPS / XPS — these are stable at room temperature. Long-term UV exposure makes EPS yellow + brittle over years; XPS holds up better.
EPP and PE can take a permanent set if you compress them for weeks (e.g. a foam part stored under heavy boxes). For long-term archival of cut parts: store loose, away from direct sunlight, away from solvent vapours.
If you want zero shrink: use polystyrene-bead-based EPS over expanded grades — beads have already done all the expanding they're going to.
EPP and PE can take a permanent set if you compress them for weeks (e.g. a foam part stored under heavy boxes). For long-term archival of cut parts: store loose, away from direct sunlight, away from solvent vapours.
If you want zero shrink: use polystyrene-bead-based EPS over expanded grades — beads have already done all the expanding they're going to.