Subsist rhymes with:
assist, cist, consist, cyst, desist, insist, persist, assist, baptiste, chryst, cist, coexist, consist, crist, cyst, delist, desist, dismissed, enlist, exist, fist, frist, ghrist, gist, grist, hissed, insist, kissed, kist, krist, list, liszt, missed, mist, nist, persist, pissed, preexist, quist, reminisced, resist, rist, schist, tryst, twist, vist, wist, wrist
Subsist sounds like:
safest, savaged, savasta, savviest, scapegoat, scapegoated, sebesta, spaced, spacesuit, spaghetti, specht, speight, spiced, spight, spigot, spiked, spooked, sposato, sposito, subacute, subject, subjected, subjugate, subjugated, subset, subside, subsided, subsidy, substitute, substituted, sufficed, suffocate, suffocated, suffused, supposed, suspect, suspected