Why would the exchange run into problems in such a case? Some are certainly more reputable than others, but for the most part there's no reason to worry there.
As well as the reasons mentioned by others, Bitfinex in particular is an exchange that is in deep financial difficulties. It has no working banking partners for anyone to withdraw USD, and their pseudo-$ currency 'Tether-USD' is rumoured to be massively over-issued to cover their account shortfalls.
Questions around the solvency of bitfinex have been circulating for years. Do they even allow USD withdrawals at present? Their actions are weirdly reminiscent of the long fall of mt gox.
There are failure modes that have plagued exchanges for centuries. Namely, when things go down (a) lots of activity happens in a short period of time, often leading to administration and technical failures, and (b) lots of people lose money which presages them (i) refusing to pony up and (ii) suing.
