A majority does not let an attacker steal coins from arbitrary wallets or forge signatures. What it permits is rewriting recent history: mining a private chain and publishing it to replace the public one, undoing deposits already credited elsewhere. That is a double-spend, and exchanges are the usual victims.
Cost scales with hash-rate or staked value, so it is impractical on the largest chains and cheap on small ones. Several smaller proof-of-work networks have been attacked repeatedly, after which exchanges raise confirmation requirements or delist them.
Under proof-of-stake the equivalent requires a majority of stake, and an attacker's own capital is destroyed by slashing when caught, which changes the economics from spending money to burning it. Neither model makes attack impossible; both make it expensive.
Related: double-spend, hash-rate, chain-reorg, confirmation