A market crash won't affect your cash held with your broker - however if the broker defaults (goes bankrupt), you may lose some or all of that cash.
If you read the customer agreement that you signed when opening the account, it's very likely that there's a clause that stipulates that under certain circumstances, the broker has the right to use your cash and/or your positions without notice. If the broker default you may not be able to recover the assets they've been using.
As an example, look at clause 14 of the Interactive Brokers US customer agreement. This is a fairly standard clause.
Depending on your jurisdiction, you may have a partial or full legal protection against such an event (e.g. the SIPC protection for US-based brokers which would apply to you if your broker is IB LLC, even if you are not a US resident/citizen).