The participant doesn't necessarily have to furnish proof of the expense to the plan administrator at the time the hardship is requested - the plan can rely on a summary substantiation.
There are plenty of other issues raised by allowing a hardship before the expense is actually incurred. For example:
What if their insurance changes next year, and covers the drug?
What if their doctor decides to change to a different drug?
What if they get better?
While there is not, strictly speaking, a requirement that the participant incur the expense before the hardship withdrawal is made, if the participant ends up not having the expense after the plan already made a distribution, then there is a qualification problem.
Within the plan, if loans are available, then that might help get the participant at least part of the way.
Outside of the plan, as someone who's been in a similar situation in the past, I'd recommend that they call the drug manufacturer. Often they have programs where they will offer the drug at a discounted price and/or on a payment plan to people whose insurance doesn't cover it. Some states also offer a charity care program which this person might be eligible for.